noahsline123
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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.

Respuesta :

mhanifa

Answer:

  • 0.21

Step-by-step 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
  • Find values at n=1 and 5 then subtract

[tex]\\ \tt\hookrightarrow g(1)=10(1.02)^1=10(1.02)=10.2[/tex]

[tex]\\ \tt\hookrightarrow g(5)=10(1.02)^5=11.04[/tex]

Subtract:-

[tex]\\ \tt\hookrightarrow 11.04-10.2[/tex]

[tex]\\ \tt\hookrightarrow 0.84[/tex]

Average rate of change:-

  • 0.84/5-1=0.84/4=0.21