6.1
Both sides……
Evaluate the expression for (a) x
1.
3
x
2.
5•2
= -2 and (b) x = 3
x
3.
3 + 2x
4.
5x
5.
10 • 2x
6.
3x – 3
Tell whether the function represents exponential growth or exponential decay. (graph #8, 10, 12)
7.
y = 5x
8.
y = 3x
9.
10.
y = (3/2)x
11.
y = (1.6)x
12.
In Exercises 10 and 11, use the graph of
13.
14.
y = (1/5)x
y = (0.5)x
f(x) = bx to identify the value of the base b.
15.
16.
In the next two problems a) Identify the annual percent increase/decrease in the value, b) what the original value was, and
c) estimate when the value will be…..
17. The value of a rare coin y (in dollars) can be
18. The value of a truck y (in dollars) can be
approximated by the model y = 0.25(1.06)t where
approximated by the model y = 54,000(0.80)t
t is the number of years since the coin was minted.
where t is the number of years since the truck was new.
(value = $0.60)
(value = $30,000)
Rewrite the function in the form
19.
y = a(3) t/2
y = a(1 + r)t or y = a(1 – r)t Then state the rate.
3t
1
4t
20. y = a(0.4)
21. y = a( /4)
22. y
= a(4/3) t/18
23. You deposit $3000 into a bank account that pays 1.25% annual interest, compounded semi-annually. How much
interest does the account earn after 4 years?
24. Now say your best friend deposit the $3000 into a different bank account with that same interest rate of 1.25% at the
same time you make your bank deposit, but her rate is compound it monthly. How much interest does the account
earn after the same 4 year period? Who got the better deal?
6.2
Both sides……
Simplify the expression.
1.
e2 • e5
2.
e-3 • e8
3.
5.
(3e3x)2
6.
√16 7.
9.
√20 10.
(5e-4x)3
11.
12e5
36e2
4.
e-9 • e7
8.
√64 12.
15e4
3e9
27e4
18e7
e2x • e5 • ex – 2
Describe and correct the error in simplifying the expression.
13.
14.
Tell whether the function represents exponential growth or exponential decay. Then graph the function.
8.
y = e4x
9.
y = e-x
Use the properties of exponents to rewrite the function in the form
Then state the rate of change.
11.
y = e-0.5x
12.
y = 2e-0.2x
y = a(1 + r)t
10.
y = 4e-2x
or
y = a(1 – r)t
13.
y = 5e0.6x
16.
y = 3ex + 2
Graph the function. Then identify the domain and range.
14.
y = ex – 1
15.
y = 4ex – 1
17. You invest $4000 in an account to save for college.
a. Option 1 pays 5% annual interest
compounded semi-annually.
What would be the balance in the
account after 2 years?
b. Option 2 pays 4.5% annual interest c. At what time t (in years)
compounded continuously.
would Option 1 give you
What would be the balance in the
$100 more than Option 2?
account after 2 years?