Unit 2 Test Review

Converting/graphing

100

What is the base value in the following exponential equation:

4²=16

4

200

Change the following equation from logarithmic to exponential:

log₅125=3

5³=125

300

List the type of function as well as the transformations of the following exponential equation compared to its parent function:

f(x)=-2(3)^x-4+5

Exponential growth

Reflected over x axis

Stretch of 2

Right 4

Up 5

400

Convert the logarithmic function to exponential

Ln 27=x

e^x=27

500

List the transformations and the asymptotes of the following equation:

f(x)=1/4log₆(x+3)+4

Log growth

compression 1/4

left 3

up 4

Vertical asym x=-3

Word Problems

100

What formula should be used for the following equation:

Lisa invested 2,000 in an account at an 1.8% interest rate compounding continuously for 10 years

A = Per^rt   or A=2,000e^0.018*10

200

Write an equation to model the following situation:

Mark invested 20 in an account at an 7% interest rate compounding bimonthly for 15 years

f(x)=20(1+(.07/24))^24*15 

^or

f(x)=20(1.0029)360

300

Becky invested $19,800 in a CD that pays an interest rate of 5.3%. The CD is set to compound daily. How much is in Becky’s account after 9 years?

$31,901.32

400

Jack bought a new car in 2014 for $28,000. If the value of the car decreases by 14% each year what will be the difference of value of the car be in 2025.

28,000-5,328.94=

22,671.06

500

A savings account balance is compounded continuously. Find the interest rate per year if the initial balance was $1,854.00 and it sat in an account for 5 years totaling to $2,154.04? 

1854e^{0.03 x 5} ≈ $2,154.04

Solving Equations

100

Solve for be rounding to the nearest hundredth:  

3^b= 17

*Remember, in order to solve a variable trapped in the exponent, you must use LOGS!

2.58

200

Solve for x round to the nearest tenth: 

5 ⋅ 18^6x = 26

0.1

300

Solve for n rounding to the nearest hundredth: 

16^n-7+ 5 = 24

8.06

400

solve for x

log₃(2)+2log₃(x)=log₃(7x-3)

x=1/2 and x=3

500

Solve for x:

3^2x=27^x-4

x=12

Expanding and Simplifying Logarithms

100

Expand this Log: 

log(3x⁴y⁷)

log(3) + 4log(x) +7log(y)

200

Simplify this Log: 

2log₄(x) + 5log₄(y) - 1/2log₄(z)

log₄(x²y⁵ / z^1/2) 

300

Expand this Log (keep as ln): 

ln(4x³/y)

ln 4 + 3 ln x  - ln y 

400

Simplify this Log: 

7 ln x + 2 ln y

ln (x⁷y²) 

500

Double Jeopardy

Jon invested $5,000 dollars into an account with an interest rate of 15% compounded continuously. Approximately how long will it take the investment to triple?

7 years

Mystery

100

Solve: 

log (5x) = log (2x + 9)

3

200

Solve and give your answer as a fraction: 

−2log₅ (7x) = 2

1/35

300

Solve: 

−6log₃ (x − 3) = −24

84

400

Solve: 

log₁₀ (2) + log₁₀ (x) = 1

5

500

The half-life of a radioactive isotope is 4 days. If 3.2 kg are present now, how much will be present after 4 days?

1.6kg