Ch. 5 Test Review

Let's Talk Logs

100

Evaluate log₆(1)

0

200

Evaluate log₃(1/9)

-2

300

Evaluate log₃(81)

4

400

Evaluate log₄(1/64)

-3

500

What is the base of ln(5)

e

Powered Up

100

Rewrite in logarithmic form: 7⁴=2401

log₇2401=4

200

Rewrite in exponential form: log₂8=3

2³=8

300

What is the base of log(2)

10

400

What is the base of log₇x?

7

500

What is the direction that y=log(x)-3 is shifted?

down 3

X Marks the Spot

100

5^x+7=42

x = 2.209

200

log₄(x+2)=3

x=62

300

log₃(x-4)=log₃(3x+6)

x=-5

400

Change to logarithmic form: (1/32)³=-2

log_(1/32)(-2)=3

500

Emma invests $25,000 in an account that pays 8% interest, compounded continuously. The amount of money in the account, P, over a period of t years can be estimated by 𝑃 = 25,000e^0.08t . In approximately how many years will it take the investment to reach $75,000?

t=13.7 years

On the Rise...Or Not

100

Growth or Decay: y=3(0.6)^x

Decay

200

Growth or Decay: y=2(1.2)^x

Growth

300

Growth or Decay: y=5e^-x

Decay

400

The population of rabbits in a controlled environment is given by P(x) = 200(0.75)ˣ, where x represents the number of months. Determine the percent rate of change for the population of rabbits per month.

Decrease of 25%

500

The equation 𝐴(ℎ) = 100(0.87)^t represents the “t” number of bacteria, 𝐴, present after 𝑡 hours after an antibacterial medication is applied. The amount of the substance decreases by ____% each hour.

13%

Let's Go to Work

100

Sarah created this equation to calculate the value, in dollars, of an investment at the end of t years: 1200(1.03)ᵗ = 1800. What investment calculation is Sarah making?

Sarah is calculating how long it will take an investment of ___________ to __________ by __________ with an interest rate of ____________.

$1200, increase, $600, 3%

200

Jayden is observing the population of a bacterial culture. The culture begins with 80 bacteria and increases by 30% each hour. Write a function that can be used to determine the bacterial culture population after x hours.

y=80(1+.30)^x 

y=80(1.3)^x

300

In 2021, a city's population was 35,250. The city uses the function P(t) = 35,250(1.03)ᵗ, where t = 0 corresponds to the year 2021, to model the future population. What is the most reasonable prediction of the city's population in the year 2026?

P(5) = 40,864

400

The function 𝑓(𝑥) = 5(1/3)^x-2+1 has which transformations from the parent function?

Vertical stretch by 5, right 2, up 1

500

A student's first step in solving the equation 3^x+2 = 9 was to rewrite 9 as 3². Solve the equation. Justify each step.

1. rewrite 9 as 3²

2. since bases are the same, drop exponents

3. subtract 2 from both sides

4. x = 0