Question

The radioactive substance uranium-240 has a half-life of 14 hours. The amount A(t) of a sample of uranium-240 remaining (in grams) after T hours is given by the following exponential function. A(t)=2400(1/2)^t/14Find the amount of the sample remaining after 7 hours and after 40 hours.Round your answers to the nearest gram as necessaryAmount after 7 hours: grams Amount after 40 hours: grams

Answer 1

Given the Exponential Function:

`A(t)=2400((1)/(2))^{(t)/(14)}^`

You know that it represents the amount A(t) of a sample of uranium-240 remaining (in grams) after "t" hours.

• Then, in order to calculate the amount of the sample remaining after 7 hours, you need to substitute this value into the function and evaluate:

`t=7`

You get:

`A(7)=2400((1)/(2))^{(7)/(14)}\approx1697`

• In order to calculate the amount of the sample remaining after 40 hours, you need to substitute this value into the function and evaluate:

`t=40`

You get:

`A(7)=2400((1)/(2))^{(40)/(14)}\approx331`

Hence, the answer is:

• Amount after 7 hours:

`1697\text{ }grams`

• Amount after 40 hours:

`331\text{ }grams`