NG_AL2_M_3_Day2_MathCast_PD
Screen
#
Using Exponential Equations to Solve Word Problems
Onscreen Elements
Bumper images with MathCAST
title: Using Exponential Equations to
Solve Word Problems
Programming/Animation Notes
N/A
Tailored bumper swf
Video file name:
I can use what I’ve learned about
exponents and logarithms to solve a real
world problem.
I have some money that I’m investing in an
account. I want to know how long I have to
leave it in the account before I will earn
$1500.
1
Whiteboard
2a
Audio Narration
Suppose $1200 was invested into
an account that pays 3.24%
interest compounded annually. In
how many years will the balance
reach $1500?
Storyboards v.1.2
Fade up from black.
Wide shot of the front of Jai Young
sitting at a table. Window view of a city
behind her. Zoom in to tight shot as
she begins to think out loud.
N/A
Transition to whiteboard
I am going to solve this problem.
<pause>
Suppose one thousand two hundred
dollars was invested into an account that
pays three point two four percent interest
compounded annually. In how many years
will the balance reach one thousand five
hundred dollars?
Add question to whiteboard in sync
with narration.
to PROD
Sound
Effects
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NG_AL2_M_3_Day2_MathCast_PD
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2b
Using Exponential Equations to Solve Word Problems
Onscreen Elements
Audio Narration
Suppose $1200 was invested into
an account that pays 3.24%
interest compounded annually. In
how many years will the balance
reach $1500?
𝑟 𝑛𝑡
𝐴 = 𝑃 (1 + )
𝑛
A = amount accumulated
P = principal amount
r = annual interest rate
n = number of times per year
interest is compounded
t = the number of year the amount
is deposited
2c
Suppose $1200 was invested into
an account that pays 3.24%
interest compounded annually. In
how many years will the balance
reach $1500?
 r
A  P 1  
 n
nt
I will substitute the values I know into the
formula.
A equals one thousand five hundred.
P equals one thousand two hundred
Trate equals 0.0324 changed the percent
to a decimal.
Sound
Effects
Add equation in sync with narration.
Add what each variable represents.
Continue to add to the given equation
in sync with narration.
N equals one since it is compounded
annually
I will be solving for t.
a = 1500
P = 1200
r = 0.0324
n=1
1t
 0.0324 
1500  1200 1 

1 

Storyboards v.1.2
I can use the compound interest formula.
Remember compound interest is your
interest earning interest.
<pause>
𝐴 equals 𝑃 times the quantity 1 plus 𝑟
divided by 𝑛 raised to the 𝑛 times 𝑡 power.
Remember that A is the amount
accumulated.
P is the principal amount (the initial
amount you borrow or deposit)
r is the annual rate of interest (as a
decimal)
n is the number of times the interest is
compounded per year
t is the number of years the amount is
deposited
Programming/Animation Notes
So now I have
<pause>
One thousand five hundred is equal to one
thousand two hundred times the quantity
one plus zero point zero, three, two, four
divided by 1 raised to the 1 times 𝑡 power.
to PROD
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2d
Using Exponential Equations to Solve Word Problems
Onscreen Elements
Suppose $1200 was invested into
an account that pays 3.24%
interest compounded annually. In
how many years will the balance
reach $1500?
 r
A  P 1  
 n
1t
Suppose $1200 was invested into
an account that pays 3.24%
interest compounded annually. In
how many years will the balance
reach $1500?
 r
A  P 1  
 n
nt
1t
 0.0324 
1500  1200 1 

1 

1500  1200(1  0.0324) t
Programming/Animation Notes
I can simplify the equation.
<pause>
In parentheses the zero point zero three
two four over one is just the decimal itself.
Continue to add to the given equation
in sync with narration.
Sound
Effects
So now I have One thousand five hundred
is equal to one thousand two hundred
times the quantity 1 plus zero point zero,
three, two, four raised to the 𝑡 power.
nt
 0.0324 
1500  1200 1 

1 

1500  1200(1  0.0324)t
2e
Audio Narration
I can drop the parentheses by adding the
one and the decimal. I can also divide
both sides by one thousand two hundred
and I have
one point two five is equal to one point
zero, three, two, four raised to the 𝑡 power.
This is an exponential equation.Since it is
not easy to find the values of t I will use
logarithms to solve.
Continue to add to the given equation
in sync with narration.
1.25  1.0324t
Storyboards v.1.2
to PROD
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2f
Using Exponential Equations to Solve Word Problems
Onscreen Elements
Suppose $1200 was invested into
an account that pays 3.24%
interest compounded annually. In
how many years will the balance
reach $1500?
 r
A  P 1  
 n
Audio Narration
Programming/Animation Notes
I will take the logarithm of both sides.
<pause>
The log of one point two, five is equal to
the log of the quantity one point zero,
three, two, four raised to the 𝑡 power.
Continue to add to the given equation
in sync with narration.
Using the properties of exponents and
logs, I can write this as a multiplication
equation.
<pause>
The log of one point two five is equal to 𝑡
times the log of one point zero, three, two,
four.
Continue to add to the given equation
in sync with narration.
Sound
Effects
nt
1t
 0.0324 
1500  1200 1 

1 

1500  1200(1  0.0324) t
1.25  1.0324t
log1.25  log(1.0324t )
2g
Suppose $1200 was invested into
an account that pays 3.24%
interest compounded annually. In
how many years will the balance
reach $1500?
 r
A  P 1  
 n
nt
1t
 0.0324 
1500  1200 1 

1 

1500  1200(1  0.0324)t
1.25  1.0324t
log1.25  log(1.0324t )
log1.25  t log(1.0324)
Storyboards v.1.2
to PROD
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NG_AL2_M_3_Day2_MathCast_PD
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#
2h
Using Exponential Equations to Solve Word Problems
Onscreen Elements
Suppose $1200 was invested into
an account that pays 3.24%
interest compounded annually. In
how many years will the balance
reach $1500?
 r
A  P 1  
 n
nt
Audio Narration
Programming/Animation Notes
I’ll divide both sides of the equation by the
log of one point zero, three, two, four
<pause>
The log of one point two five divided by the
log of one point zero, three, two, four is
equal to 𝑡.
Continue to add to the given equation
in sync with narration.
Sound
Effects
Animation: You can scroll off one line of the
problem at a time, starting at the top, as
though we are scrolling down to reveal
additional lines of the equation.
After the log 1.25 = log (1.0324t)
1t
 0.0324 
1500  1200 1 

1 

1500  1200(1  0.0324)t
At some point, this becomes way
too much text to leave onscreen. Consider
removing top lines of the worked
equation up to 1.25 = 1.0324^t once the
equation is written in logarithmic form.
You can scroll off one line of the problem
at a time, starting at the top, as though
we are scrolling down to reveal additional
lines of the equation.]
[TECH:
1.25  1.0324t
log1.25  log(1.0324t )
log1.25  t log(1.0324)
log1.25
t
log1.0324
Storyboards v.1.2
to PROD
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NG_AL2_M_3_Day2_MathCast_PD
Screen
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2i
Using Exponential Equations to Solve Word Problems
Onscreen Elements
Suppose $1200 was invested into
an account that pays 3.24%
interest compounded annually. In
how many years will the balance
reach $1500?
 r
A  P 1  
 n
nt
Audio Narration
Programming/Animation Notes
Using my calculator to divide t is about
seven .
Continue to add to the given equation
in sync with narration.
It will take About 7 years for the balance to
reach one thousand five hundred dollars.
Sound
Effects
If possible show the graphing
calculator screen with calculation.
1t
 0.0324 
1500  1200 1 

1 

1500  1200(1  0.0324)t
1.25  1.0324t
log1.25  log(1.0324t )
log1.25  t log(1.0324)
log1.25
t
log1.0324
It will take about 7 years for the
balance to reach $1500.
Storyboards v.1.2
to PROD
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Onscreen Elements
Using Exponential Equations to Solve Word Problems
Audio Narration
Programming/Animation Notes
Sound
Effects
3a
I can use what I know about exponents
and logarithms to find how long it will take
me to reach a financial goal.
Transition back to Jai Young sitting at
the dining room table with pad of grid
paper on table and pencil in hand.
Fade out graphic box and return to
smiling Jai Young at the table – close
up shot of face.
Fade to black.
Storyboards v.1.2
to PROD
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