Answer:
C. 5 should be replaced with 1/2, and t/2 should be replaced with t/5
Step-by-step explanation:
The problem statement tells you the half-life of the car is 5 years. Using the value h = 5 in the given equation, you have ...
m(t) = m₀(1/2)^(t/5)
The problem statement tells us the initial value of the car is $20,000, so we have ...
m₀ = 20000
m(t) = 20000(1/2)^(t/5)
Since Andrew wants the value of t when m(t) = 15000, his equation would read ...
15000 =20000(1/2)^(t/5) . . . equation for finding when the value is 15000
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The equation Andrew proposes to solve is ...
20000(5)^(t/2) = 15000
In order to make his equation look like the the one above, the changes should be ...
5 should be replaced with 1/2, and t/2 should be replaced with t/5.
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<em>Additional comment</em>
The equation can be solved as follows:
15000/20000 = (1/2)^(t/5)
log(3/4) = (t/5)log(1/2) . . . . take the log of both sides, simplify the fraction
t = 5log(3/4)/log(1/2) . . . . divide by the coefficient of t
t ≈ 2.08
Andrew's car will have a value of about $15,000 after 2 years and 1 month.
