Question

A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 12(1.03)n

What is the average rate of change of the function f(n) from n = 3 to n = 10, and what does it represent? (4 points)

Answer 1

Answer:

The average of rate was of 0.4314 cm/day, which means that on average, during this interval, the plant grew by 0.4314 cm each day.

Step-by-step explanation:

Average rate of change:

The average rate of change of a function f(x), from x = a to x = b, is given by:

$A = \frac{f(b)-f(a)}{b-a}$

In this question:

$f(x) = 12(1.03)^n$

From n = 3 to n = 10

$a = 3, b = 10$

$f(b) = f(10) = 12(1.03)^{10} = 16.13$

$f(a) = f(3) = 12(1.03)^{3} = 13.11$

Average rate of change:

$A = \frac{f(b)-f(a)}{b-a} = \frac{16.13-13.11}{10-3} = 0.4314$

The average of rate was of 0.4314 cm/day, which means that on average, during this interval, the plant grew by 0.4314 cm each day.