#31 Exponential Real World Applications

An experiment begins with 20 grams of a radioactive isotope. This isotope has a half-life. If y is the mass in grams remaining after x half-lives have elapsed, which equation represents the amount of grams the isotope will weigh after 4 half-lives?

A population of ants increases by a factor of 5 each year. Initially there were 450 aunts. Which equation represents the amount of aunts after 9 years?

Let y represent the total amount of aunts after x years.

The population of wild yellow-eyed baboons living in a forest quadruples every year. If there are 24 baboons living in the forest today, how many will there be in 3 years?

*Use google calculator.

• 1,944

• 55,296

• 192

• 1,536

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

Is y = 54(.20)^x growth or decay?

• Growth because of the 54
• Decay because of the .20
• Decay because of the 54
• Growth because of the .20

You have inherited land that was purchased for $30,000 in 1990. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?

• $83,579
• $10,217
• $14,963,655
• $28,500

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

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)³
• y = 7650(1.14)³

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?

An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%.

What is the multiplier (b) for this problem?

• 1.29

• .29

• .71

• 1.71