9514 1404 393
Answer:
1. 3(0.96059601^t) = 15; t = -40.03
2. 4.121204(1.01^t) = 8; t = 66.66
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
The solution for an exponential problem using logarithms is ...
a·b^x = c ⇒ log(c/a)/log(b) = x
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1. Rewrite: (3)(0.99^4)^t = 15 ⇒ 3(0.96059601^t) = 15
Solution: t = log(15/3)/log(0.96059601) ≈ -40.03
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2. Rewrite: 4(1.01^3)(1.01^t) = 8 ⇒ 4.121204(1.01^t) = 8
Solution: t = log(8/4.121204)/log(1.01) ≈ 66.66
