Question

The percentage of people in a certain country who earn at least t thousand dollars, 25 ≤ t ≤ 150, can be modeled as p(t) = 119.931(0.963t)percent.Is p increasing or decreasing on the interval 25 ≤ t ≤ 150?

Answer 1

The function p(t) = 119.931(0.963t) percent is neither increasing nor decreasing on the interval 25 ≤ t ≤ 150.

Step-by-step explanation:

The given function is p(t) = 119.931(0.963t) percent.

To determine if p(t) is increasing or decreasing on the interval 25 ≤ t ≤ 150, we need to find the derivative of p(t) and check its sign.

Let's differentiate p(t) with respect to t:

1. Apply the power rule: differentiate 0.963t as 0.963.
2. Factor out the constant 119.931.

The derivative of p(t) is p'(t) = 0.963 * 119.931.

Since p'(t) is a constant, it is neither positive nor negative. Therefore, p(t) is neither increasing nor decreasing on the interval 25 ≤ t ≤ 150.