Question

The decay of 230 mg of an isotope is described by the function A(t)= 230e-0.031t, where t is time in years. Find the amount left after 26 years. Round your answer to the nearest mg.

Answer 1

The function is
A(t) = 230×e^(-0.031t)
A the amount left after 26 years ?
230 the current amount
E constant
-0.031 rate of decreases each year
T time 26 years

A (26)= 230×e^(-0.031×26)
A (26)= 102.72 round your answer to get 103

Hope it helps!

Answer 2

103 mg.

Explanation:

We have been given that the decay of 230 mg of an isotope is described by the function
`A(t)=230e^(-0.031t)`, where t is time in years.

To find the amount left after 26 years, we will substitute
`t=26` in our given function as:

`A(26)=230e^(-0.031\cdot 26)`

`A(26)=230e^(-0.806)`

Using exponent property
`a^(-n)=(1)/(a^n)`, we will get:

`A(26)=230* (1)/(e^(0.806))`

`A(26)=(230)/(e^(0.806))`

`A(26)=(230)/(2.2389343)`

`A(26)=102.72744\approx 103`

Therefore, 103 mg of isotope will be left after 26 years.