Question

100 Points for some help

A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days.

g(n) = 10(1.02)

What is the average rate of change of the function g(n) from n=1 to n=5? Please show all work.

Answer 1

• Find values at n=1 and 5 then subtract

`\\ \tt\hookrightarrow g(1)=10(1.02)^1=10(1.02)=10.2`

`\\ \tt\hookrightarrow g(5)=10(1.02)^5=11.04`

Subtract:-

`\\ \tt\hookrightarrow 11.04-10.2`

`\\ \tt\hookrightarrow 0.84`

Average rate of change:-

• 0.84/5-1=0.84/4=0.21

Answer 2

• 0.21

Explanation:

Given equation:

• g(n) = 10*(1.02)ⁿ

Find the difference of g when n = 1 and n = 5:

• g(5) - g(1) =
• 10*(1.02)⁵ - 10*(1.02)¹ =
• 0.84 (rounded)

Divide the above number by the difference of 5 and 1:

• 0.84 / (5 - 1) =
• 0.84 / 4 =
• 0.21