Chapter 8: Exponentials & Logarithms “I CAN” statements
Name:
Directions: Identify each of the following “I CAN” statements you know you have mastered. Write the entire statement out on your
paper then do the PROVE IT problem(s). Show your work. After you’ve done all of the statements you are sure about, go back and
work on the statements you need to improve upon. With each of these you should do the IMPROVE IT problem(s) then write the
“NOW I CAN” statement.
NOTE: SGPW refers to the Study Guide and Practice Workbooks available in the classroom.
I can…….
Problems to prove or improve my skills
1
Recognize exponential growth and decay in an equation.
Prove it: p. 829 #11 & #13 Improve it: p. 425 Example 4 parts a-c
2
Find the growth or decay factor (“b” in the exponential
equation).
Find the percent of increase or decrease that a
function models.
Prove it: +45% and -10%
Improve it: Top of p. 423 & p. 426 Ex 6 then p. 428 #50,51
3
Prove it: y = 1700(0.75) x and y = 984.5(1.73) x
4
Write an equation for exponential growth.
Improve it: Top of p. 423 & p. 426 Ex 6 then p. 427 #38,39
Prove it: SGPW p. 104 #12 Improve it: SGPW p. 103 Example and #1
5
Write an equation for exponential decay.
Prove it: SGPW p. 104 #10 Improve it: SGPW p. 103 Example and #3
6
Write an exponential equation given two points or a
graph.
I can identify the parent function and vertical and
horizontal shift.
Find the balance in an account when interest is
compounded n times per year
Write and evaluate an equation for a half-life problem.
Prove it: p. 829 #4, p. 427#32 Improve it: p. 424 Ex 3 then check
understanding
Prove it: p.434 #12: Identify parent function and shift. Improve it: Read top
of p. 432 and compare graphs pictured in Example 2.
Prove it: PG. 436 #40a
7
8
9
x
10
Evaluate e
11
13
Write and evaluate an equation for continuously
compounded interest problems.
Find the difference between balances when
compounding continuously and compounding periodically.
Write an exponential equation in logarithmic form.
14
Evaluate logarithms.
12
Prove it: SGPW p. 106 #8 Improve it: p. 432 Ex 3 then check understanding
Prove it: Evaluate e3/2 Improve it: p. 433 Ex. 4, then check understanding
Prove it: SGPW p. 106 #6
Improve it: p. 434 Ex 5 then check understanding
Prove it: PG. 436 #40b
Prove it: p. 829 #24 & #28 Improve it: p. 439 Ex 2 then check
understanding
Prove it: Evaluate log 4 64 and log 8 2
Improve it: SGPW p. 107 Example and #1,4 and 7
15
Write a logarithm in exponential form.
Prove it: Write x = log 3 8 in exponential form.
16
Find the inverse of a logarithmic function.
Improve it: SGPW p. 107 Example and #10, 19
Prove it: Find the inverse of y = log5x Improve it: p. 402 Ex 2 then p. 443
#71
17
Identify all three properties of logarithms.
Prove it: SGPW p. 110 #41-#43 Improve it: p. 471 top of page then #48 & 50
18
Expand and condense logarithms using the product
property.
Prove it: Expand log 2 xyz & rewrite log 5 4 + log 5 3 as a single log.
19
Expand and condense logarithms using the quotient
property.
Improve it: p. 471 top of page then #44
Prove it: Expand log 3
x
& rewrite log 6 25 − log 6 5 as a single log.
yz
Improve it: p. 471 top of page then #45
20
21
22
Expand and condense logarithms using the power
property.
Expand and condense logarithms using a combination
of the properties.
Use the properties of logarithms to evaluate an
expression.
Prove it: Expand log 4 (2 x) 3 & rewrite 5 log x + 3 log x 2 as a single log.
Improve it: p. 471 top of page then #51
Prove it: p. 829 #45 & #49
Improve it: p.447 Ex 1 through Ex 3 then p. 829 #45 & #49
Prove it: Evaluate 2 log 8 4 −
1
log 8 8
3
Improve it: p. 447 Ex 1 through Ex 3 then do the “prove it” problem.
23
Solve an exponential equation using graphing.
Prove it: Solve 1.5 =356 Improve it: p.454 Ex 4 check understanding
24
Solve an exponential equation using logarithms.
Prove it: p. 829 #54 Improve it: SGPW p. 111 Example and #5
25
Use the Change of Base Formula.
Prove it: Find log 3 40 rounded to the nearest hundredth
26
Solve a logarithmic equation.
Improve it: p. 453 Key Concept then p. 454 Ex 2 check understanding part a
Prove it: p. 829 #60 Improve it: p. 455 Ex 6 check understanding
27
Use logarithmic properties to solve an equation.
Prove it: p. 829 #61 Improve it: p. 456 Ex 7 check understanding
28
Apply logarithmic properties to formulas to solve.
Prove it: p. 465 #40 Improve it: p. 448 Ex 4 check understanding
29
Find an exponential model of best-fit using my
calculator.
Simplify natural logarithms.
Prove it: p. 467 #70 part b Improve it: p. 430 Example then #2
30
x
Prove it: Write ln a − 2 ln b +
1
ln c as a single log.
2
31
Solve natural logarithmic equations.
Improve it: p. 462 Ex 1 check understanding
Prove it: p. 829 # 59 Improve it: p. 463 Ex 3 check understanding
32
Solve exponential equations using natural logs.
Prove it: p. 829 # 58 Improve it: SGPW p. 113 Example and #4