Part A → Domain of the growth function → [0, 5]
Part B → y-intercept means height of the plant at the start of the
experiment (n = 0).
Part C →Average rate of change of the function will represent the change
in the height of the plant per year.
Growth function for the height of the plant has been given as,
f(n) = [tex]10(1.02)^n[/tex]
Here, n = Number of years
f(n) = height of the plant after 'n' years
Part A
If the f(n) = 11.04 cm
By substituting the value in the equation,
[tex]11.04=10(1.02)^n[/tex]
[tex](1.02)^n=1.104[/tex]
Take log on both the sides,
[tex]\text{log}(1.02)^n=\text{log}(1.104)[/tex]
n[log(1.02)] = log(1.104)
n = 4.996 ≈ 5 years
Therefore, span of the study was 0 years to 5 years.
So domain to plot the growth function will be [0, 5].
Part B.
For y-intercept → n = 0,
f(0) = 10(1.02)⁰
f(0) = 10 cm
Therefore, y-intercept means length of the plant at the start of the experiment.
Part C.
Average rate of change of the function from n = 1 to n =5,
Average rate of change = [tex]\frac{f(5)-f(1)}{5-1}[/tex]
= [tex]\frac{11.04-10}{5-1}[/tex]
= 0.26 cm per year
Therefore, average rate of change of the function will represent the change in height of the plant per year and this change for the experiment was 0.26 cm per year.
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