Exponential Compounding Word Problems

Write an equation for this problem:

A population of 1200 bacteria is doubling each day for x days.

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?

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?

• $361,223.09

• $15,000.00

• $31,500.29

• $280,500.86

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 hen simplify inside the parenthesis)

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x

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

James' 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.

• y = 70(2)³⁵

• y = 70(2)⁵

• y = 2(70)⁵

• y = 5(70)²

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.

• y=6(0.14)^x

• y=6(1 + 14)^x

• y=6(1 + .14)^x

• y=6(0.86)^x

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

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