Problem 1
Answer: 25% growth
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Explanation:
The base of the exponent 1.25 is in the form 1+r with r = 0.25
r = 0.25 converts to 25%
The fact that r is positive indicates we have growth.
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Problem 2
Answer: 80% decay
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Explanation:
Rewrite 5^(-t) as (1/5)^t. The negative exponent has us apply the reciprocal of the base. The rule is x^(-k) = (1/x)^k = 1/(x^k)
Then we write 1/5 as 0.2 and set it equal to 1+r. Solve for r
1+r = 0.2
r = 0.2-1
r = -0.8
The negative r value tells us we have decay.
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Problem 3
Answer: 1.7% growth
This value is approximate
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Explanation:
(1.20)^(t/11) = (1.20^(1/11))^t
(1.20)^(t/11) = (1.0167128)^t .... use calculator, this is approximate
Set 1.0167128 equal to 1+r and solve for r
1+r = 1.0167128
r = 1.0167128-1
r = 0.0167128
r = 1.67128%
r = 1.7%
The positive r value tells us we have growth.
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Problem 4
Answer: 37% decay
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Explanation:
Set the base 0.63 equal to 1+r and solve for r
1+r = 0.63
r = 0.63-1
r = -0.37
r = -37%
The negative r value indicates decay.
