Question

The number of new visits to a website is decreasing exponentially. It can be modeled by the function h(d)=2170(0.92)^d, where h is the number of new site hits and d is the number of days since the site opened. Which of the following is the average rate of change of h over the interval 2≤d≤4?

1)-141 hits per day
2)-282 hits per day
3)71 hits per day
4)210 hits per day
Please explain how you did this thanks

Answer 1

2) -141 hits/da

Explanation:

Calculate the values of h(2) and h(4)

h(2) = 2170(0.92)² = 2170 × 0.8464 = 1837

h(4) = 2170(0.92)⁴ = 2170 × 0.7164 = 1555

Calculate the average rate of change

Rate of change = (y₂ - y₁)/(x₂-x₁) = (1555 -1837)/(4 - 2) = -282/2 = -141 hits/da

The average rate of change is -141 hits/da.

In the figure below, the red curve represents the function h(d), while the green dashed line represents the average rate of change over the interval 2 ≤ d ≤4.