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

Answer:

$57.2\ g$

Step-by-step 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

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

$f(x)=57.2\ g$