Question

One hundred grams of radium are stored in a container. The amount RR (in grams) of radium present after tt years can be modeled by R=100e−0.00043tR=100e−0.00043t. After how many years will only 5 grams of radium be present? Round your answer to the nearest whole year.

Answer 1

6967 years

Explanation:

Given the exponential function :

R=100e−0.00043t

Time = t in years

R = final amount

Number of years in which only 5 grams of radium will be present :

R = 5

Plugging into our formula :

5 = 100 * e^−0.00043t

5 / 100 = e^−0.00043t

0.05 = e^−0.00043t

Take the In of both sides

−2.995732 = - 0.00043t

t = −2.995732 / - 0.00043t

t = 6966.819

t = 6966.819 years

t = about 6967 years