Exponential Word Problems Compounding

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

• y=8(15,000)^x

• y=15,000(1.08)^x

• y=15,000(0.92)^x

• y=15,000(0.08)^x

Is this exponential growth or decay?

• Growth because a=1

• Growth because there is no a

• Decay because b=0.5

• Neither because a=0

Rapunzel's hair grew 16% each week she was in the tower. If her hair was 20 inches long when she was placed in the tower, what is a model for the growth of Rapunzel's hair?

If Jack's Bean stalk grew 75% every hour and the bean stalk was 2 foot when he started watching it grow, what is a model for the growth of the bean stalk?

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 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:

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?

• $8,881.47

• $7,432.93

• $8,400

• $6,500

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

Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour, how many bacteria will we have after half of a day?

• 1024

• 2048

• 8192

• 4096