Exponential Functions Word Problems (Growth/Decay Factor)

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?

•  $y=20\left(2\right)^4$  

•  $y=4\left(20\right)^{\frac{1}{2}}$  

•  $y=20\left(\frac{1}{2}\right)^4$  

•  $y=20\left(4\right)^{\frac{1}{2}}$  

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

The number of turkey vultures in a nature sanctuary is doubling each year. When the sanctuary opened, it was home to 204 turkey vultures. Which equation can be used to find the number of turkey vultures after x years?

• $y=204\left(x\right)^2$

• $y=2\left(204\right)^x$

• $y=204\left(2\right)^x$

• $y=x\left(2\right)^{204}$

Tags

CCSS.HSF.LE.A.2

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.

• $y=450\left(9\right)^5$

• $y=450\left(5\right)^9$

• $y=5\left(450\right)^9$

• $y=9\left(450\right)^5$

Tags

CCSS.HSF.LE.A.2

You have 40 grams of a radioactive kind of silver. How much will be left after 14 days if it triples each day?

*Use Google Calculator and shift 6 to get the exponent.

• 191,318,760

• 109,760

• 18,130,406

• 14000

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

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

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Annual sales for a fast food restaurant are $650,000 and are increasing at a factor of 1.04 per year. Use an exponential function to find the annual sales after 7 years.

• $1,000,124

• $4,030

• $855,355.66

• $434,505.66

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2