4.5 - 4.6 Quiz Review

Exponential Equations

100

Solve: 3^(x-3) = 17. Round to the nearest thousandth. 

5.579

200

Solve: 2^(x-1) = 19. Round to the nearest thousandth. 

5.248

300

Solve: 8^(3-x) = 15

1.698

400

Solve: 7^3x = 8^(x+1). Round to the nearest thousandth. 

0.553

500

Solve: 6^(x+6) = 3^x. Round to the nearest thousandth. 

-15.510

Log Equations

100

Solve: log(3 + x) - log(x - 4) = log(2)

11

200

Solve: log(3 + x) - log(x - 5) = log(3)

9

300

Solve: log₄(log₄x) = 1

256

400

Solve: log₉(x - 7) + log₉(x - 7) = 1

10

500

Solve: log(x - 9) = 1 - log(x)

10

Write the Equations

100

Using 2e^0.09t = y, where y is people in millions and x is the number of years, how large will the population be in 6 months?

Y = 2e^0.09(1/2)

200

Using 2e^0.09t = y, where y is people in millions and x is the number of years, when will the population reach 5 million?

5 = 2e^0.09t

300

Using 2e^0.09t = y, where y is people in millions and x is the number of years, how large will the population be in 7 years?

2e^0.09(7) = y

400

Using 2e^0.09t = y, where y is people in millions and x is the number of years, how long will it take for the population to double?

4 = 2e^0.09t’

500

Using 2e^0.09t = y, where y is people in millions and x is the number of years, how long will it take for the population to quadruple?

8 = 2e^0.09t

Identify Details from Equations

100

Using the expression 60,000e^0.0225t = y, identify the principal amount. 

$60,000

200

Using the expression 60,000e^0.0225t = y, identify the rate, as a percent.

2.25%

300

Using the expression 555e^0.05t = y, identify the principal amount. 

$555

400

Using the expression 555e^0.05t = y, identify the rate, as a percent. 

5%

500

Using the expression y = 77,687e^0.0675t, identify the principal amount and the rate. 

$77,687 and 6.75%