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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.

2 Answers

1 vote
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!
User Alex Tartan
by
9.3k points
5 votes

Answer:

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.

User Sandhu Santhakumar
by
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