Question

An element with mass 210 grams decays by 8.3% per minute. How much of the element is remaining after 15 minutes, to the nearest 10th of a gram?

Answer 1

`57.2\ g`

Explanation:

In this problem we have a exponential function of the form

`f(x)=a(b^x)`

where

f(x) is the remaining mass of the element in grams

x is the time in minutes

a is the initial value (y-intercept of the exponential function)

b is the base

r is the rate

`b=(1+r)`

In this problem we have

`a=210\ g`

`r=-8.3\%=-8.3/100=-0.083` ---> is negative because is a decay's rate

`b=(1-0.083)=0.917`

substitute

The exponential function is equal to

`f(x)=210(0.917^x)`

For x=15 minutes

substitute in the function

`f(x)=210(0.917^15)`

`f(x)=57.2\ g`