Question

160(0.96)^n=100

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for n in the equation 160(0.96)^n = 100, we can start by dividing both sides by 160:

(0.96)^n = 100/160
(0.96)^n = 0.625

Next, we can take the natural logarithm of both sides to solve for n:

ln(0.96)^n = ln(0.625)
n * ln(0.96) = ln(0.625)
n = ln(0.625) / ln(0.96)

Using a calculator to find the logarithms, we get:

n ≈ -3.2065 / -0.0408
n ≈ 78.49

Therefore, the solution to the equation is approximately n ≈ 78.49.