Word Problem

[kayesal]

The function A=Aoe-0.00866x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the valut. If 200 pounds of the material are initially put into the vault, how many pounds will be left after 30 years?

A = A oe-0.00866(30)
= 200 x oe-0.00866(30)

I got 59 lbs.

 

[skeeter]

try again ...

A = 200e^-.00866*30

A = 154.24 lbs

 

[soroban]

Hello, kayesal!

The function \(\displaystyle A\:=\:A_oe^{-0.00866x}\) models the amount in pounds of a particular radioactive material
stored in a concrete vault, where x is the number of years since the material was put into the valut.

If 200 pounds of the material are initially put into the vault, how many pounds will be left after 30 years?

\(\displaystyle A \:= \:A_oe^{-0.00866x}\)

\(\displaystyle A \:=\:200\,\times\,e^{-0.00866(30)}\;\;\) . . . This is correct!

I got 59 lbs. \(\displaystyle \;\;\) . . . This is not.

You may have entered it incorrectly in your calculator.

Try it again with baby-steps . . .

\(\displaystyle \;\;-0.00866(30)\:=\:-0.2598\)

\(\displaystyle \;\;e^{-0.2598}\:=\:0.771205812\)

\(\displaystyle \;\;200\,\times\, 0.771205812\:=\:154.2411623\)