Exponential Growth or Decay Word Problems

Your shiny new boat cost $7650.  The depreciation for your boat is 14% per year. Estimate the value of your vehicle in 3 years. What is the equation that models this problem?

• y= 7650(.14)³

• y= 7650(.86)³

• y= 7650(1+.86/1)^3*1

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

Someone drops a basketball from a height of 10 feet. Each time it bounces, the bounce height decreases by 1/3. Which statement is correct?

• The decay rate is 1/3

  and the decay factor is 2/3

• The decay rate is 2/3

  and the decay factor is 1/3

If 10 mg of iodine 131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days.

• 25mg

• 25g

• 10g

• 10mg

The equation that models how much Acetaminophen is in his body is y=400\left(0.86\right)^x Calculate how much medicine is left after 10 hours

• 400 milligrams

• 344 milligrams

• 89 milligrams

• 11 milligrams

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

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