Review- Exponential and Logarithmic Functions

Solve:
 $25^{x+2}=5^{3x-3}$  

• x = 2

• x = 3

• x = 4

• x = 7

Simplify  $\log_464$  

•  $\frac{1}{3}$  

• 3

• 16

• 4

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x
• y = 15(1.35)^x
• y = 15(0.35)^x
• y = 35(1.15)^x

A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population. Which function can be used to determine the number of deer, y, in this population at the end of t years?

• y = 1500(1 - 0.015)^t
• y = 1500(0.015)^t
• y = 1500(1 + 0.015)^t
• y = 1500(1.5)^t

Which of the following equations represents exponential decay?

•  $y=0.75\left(1.6\right)^x$  

•  $y=230\left(0.78\right)^x$  

•  $A=120\left(\frac{1}{2}\right)^{\frac{t}{12}}$  

•  $P=5\left(\frac{4}{5}\right)^t$  

•  $M=\frac{3}{4}\left(3\right)^t$  

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x
• y=30(5000)^x
• y=5000(1.3)^x
• y=5000x^x

What is the balance of $6000 compounded annually at a rate of 4% for 10 years?

• $8,881.47
• $7,432.93
• $8,400
• $6,500

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

• 14327
• 4309
• 839
• 7680

Treasure won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she earn in 10 years?

• $4915.59

• $3933.28

• $2979.81

• $4005.09

Cora invested $400 at a rate of 35% for 8 months, compounded continuously. How much is her investment worth after 8 months?

• $520.07

• $505.12

• $460.11

• $7,643.74