Chapter 7

7.1

100

Identify this function as an example of exponential growth or decay. Then state the y-intercept.

y=.05(6)^x

Exponential growth

y-int: (0,.05)

200

Identify this function as an example of exponential growth or decay. Then state the y-intercept.

y=30(.25)^x

Exponential decay

y-int: (0,30)

300

Calculate exponential growth if a=$1234, r=5%, and t=6 years.

$1653.68

400

You invested $2000 in a savings account that pays 7% interest. How much money will be in the account after 8 years?

$3436.37

500

You invest $5000 in a savings account with 5% interest. How many years will it take for the account to grow to at least $7000?

7 years

7.2

100

What is the asymptote of y=25(.6)^x+15?

y=15

200

What is the value of e^-2 to three decimal places?

0.135

300

-What transformations occur in the equation?

y=-3(6)^x-2

A reflection across the x-axis, a stretch by a factor of 3, and a horizontal shift 2 units right

400

You deposit $4000 in an account that pays 5% annual interest compounded continuously. How much money will you have 3 years later?

$4647.34

500

You deposit $2500 in an account that pays 8% annual interest compounded continuously. How much money will you have 5 years later?

$3729.56

7.3

100

What is the logarithmic form of the equation?

150=5²

log₅150=2

200

What is the exponential form of the equation?

log₉78=3

9³=78

300

What is the value of this logarithm?

log₄1024

log₄1024=5

400

How does the graph of y=log₄(x-4)+3 compare to the parent function? (Just describe the transformations)

It shifts the parent function 4 units right and 3 units up.

500

How many more times intense is an earthquake with a magnitude of 7.8 than an earthquake with a magnitude of 6.0? Use the formula log(I₁/I₂)=M₁-M₂ to solve.

63.1 times

7.4

100

What is the expression written as a single logarithm?

7log₃y+6log₃x

log₃x⁶y⁷

200

What is the expression written as a single logarithm?

log₄32-log₄2

2

300

What is the logarithm expanded?

log(5x/y)

log5+logx-logy

400

What is the logarithm expanded?

log₃27x²

3+2log₃x

500

What is the value of the expression using the change of base formula? (rounded to two decimal places)

log₃₂54

1.15

7.5

100

Solve the exponential equation.

27^3x=81

x=4/9

200

Solve the exponential equation.

15^2x=250

1.02

300

Solve by graphing.

8^2x=5000

2.0479521

400

What is the solution of log(3-2x)=-1?

1.45

500

What is the solution of log18-log3x=-3?

6000