Exponential Equations Half-Life Problems

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

The number of research papers in Professor Sycamore area of expertise has been increasing by 5% every year. Given that 30,010 research papers were published this year. Assuming the trend continues, which equation projects the amount of research papers published in x years?

• y = 30,010 (.05)^x

• y = 30,010 (1.05)^x

• y = 30,010 (.95)^x

• y = 30,010 (5)^x

A city doubles its size every 64 years. If the population is currently 225,000, what will the population be in 128 years?

• The population will be 225,000.

• The population will be 450,000.

• The population will be 900,000.

• The population will be 1,800,000.

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.

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

• 14,195.08 grams

• 26.2 grams

• 1.36 grams

• 2.93 grams

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

The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning, how many grams would be left after 7.2 minutes has elapsed?  

• 11.5 grams

• 12.5 grams

• 13.5 grams

• 14.5 grams