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3 years ago

Rewrite the following problems using exponent rules. Then, solve using logarithms.

Mathematics

1 answer:

Anna35 [415]3 years ago

3 0

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

_____

1. Rewrite: (3)(0.99^4)^t = 15 ⇒ 3(0.96059601^t) = 15

Solution: t = log(15/3)/log(0.96059601) ≈ -40.03

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

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