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.

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!

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ApusApus ApusApus · Answer 2 · 2019-07-15T16:09:07+02:00

Answer:

103 mg.

Step-by-step explanation:

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

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

[tex]A(26)=230e^{-0.031\cdot 26}[/tex]

[tex]A(26)=230e^{-0.806}[/tex]

Using exponent property [tex]a^{-n}=\frac{1}{a^n}[/tex], we will get:

[tex]A(26)=230\times \frac{1}{e^{0.806}}[/tex]

[tex]A(26)=\frac{230}{e^{0.806}}[/tex]

[tex]A(26)=\frac{230}{2.2389343}[/tex]

[tex]A(26)=102.72744\approx 103[/tex]

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