Half Life of Exponential Functions Word Problems

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

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?

You have 30,016 grams of radioactive kind of rubidium. How much will be left after 54 minutes if its half-life is 18 minutes?

• 15,008 grams.

• 7,504 grams

• 3,752 grams.

• 1,876 grams.

Due to its weakening steel industry, Canalave Town has been experiencing a population decline of 10% every year. The current population is 74,000 people. Assuming the trend continues, which equation projects the population in x years?

• y = 74,000 (0.10)^x

• y = 74,000 (0.90)^x

• y = 74,000 (1.10)^x

• y = 74,000 (1.90)^x

Barium has a half-life of 2 minutes. An initial sample weighing 80g was obtained. If it takes 10 minutes to set up an experiment using barium, how much barium will be left after the 10 minutes?

• 0.25g

• 2.5g

• 25g

• 80g

Estimate the half-life of the radioactive substance shown in the graph:

• 6 months

• 6 hours

• 1 year

• 1 minute

• 32 grams

• 16 grams

• 25 grams

• 31.24 grams

The half-life of chromium-51 is 28 days. If the sample contained 510 grams, how much chromium-51 would remain after 56 days?

• 127.5 g

• 164.3 g

• 23.45 g

• 287 g

The amount of cola in a soda machine decreases by a rate of 5% each hour. The amount of cola in the machine was originally 75 gallons. Which function models the amount of cola in gallons after h hours?

• f(h) = 75(-5)^h

• f(h) = -5(75)^h

• f(h) = .95(75)^h

• f(h) = 75(.95)^h