Applications of Exponential and Logarithmic Functions

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

• $y\ =\ 5000\left(1-\frac{30}{100}\right)^t$

• $y\ =\ 5000\left(1+\frac{30}{100}\right)^t$

• $y\ =\ 30\left(1-\frac{5000}{100}\right)^t$

• $y\ =\ 30\left(1+\frac{5000}{100}\right)^t$

Write an equation that models the following situation:

Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

(HINT: Write out the equation on a separate piece of paper and then simplify inside the parenthesis)

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x

You buy a new computer for $2100. The computer decreases by 50% annually. Which function represents the situation?

•  $y\ =\ 2100\left(1-\frac{50}{100}\right)^t$  

•  $y\ =\ 2100\left(1+\frac{50}{100}\right)^t$  

•  $y\ =\ 50\left(1-\frac{2100}{100}\right)^t$  

•  $y\ =\ 50\left(1+\frac{2100}{100}\right)^t$  

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. Write an equation to represent the situation:

• $f\left(x\right)\ =\ 30,000\left(1\ +\ 0.05\right)^t$

• $f\left(x\right)\ =\ 30,000\left(1\ -\ 0.05\right)^t$

Which exponential function is used to represent a word problem that is decreasing over time?

• $\ A\ =\ P\left(1+\frac{\%}{100}\right)^t$

• $\ A\ =\ P\left(1-\frac{\%}{100}\right)^t$

You invested $400 into an account with 7.5% interest rate compounded monthly. Which equation can be used to calculate how much you will have in 7 years?

• $f\left(x\right)\ =\ 7.5\left(1+\frac{400}{100}\right)^7$

• $f\left(x\right)\ =\ 400\left(1+\frac{7}{100}\right)^{7.5}$

• $f\left(x\right)\ =\ 400\left(1+\frac{7.5}{100}\right)^7$

• $f\left(x\right)\ =\ 7\left(1+\frac{7.5}{100}\right)^{400}$

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

Use the function below: $6000\left(1+\frac{4}{100}\right)^{10}$  

• $8,881.47

• $7,432.93

• $8,400

• $6,500

In the formula below:
What does P mean $A\ =\ P\left(1\pm\frac{r}{100}\right)^t$  

• Rate

• Starting Amount

• Interest as a decimal

• Final Amount

In the formula below:
What does t mean $A\ =\ P\left(1\pm\frac{r}{100}\right)^t$  

• Rate

• Starting Amount

• Interest as a decimal

• time 

In the formula below:
What does A mean $A\ =\ P\left(1\pm\frac{r}{100}\right)^t$  

• Rate

• Starting Amount

• Interest as a decimal

• Final Amount