Question

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

Answer 1

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