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

Part A: When the scientist concluded his study, the height of the plant was approximately 16.13 cm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)

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

Answer 1

Answer:

Step-by-step explanation:

A) 16.13 = 12(1.03)ⁿ

   1.344 = (1.03)ⁿ

ln(1.344) = n(ln(1.03))

           n = (ln(1.344)) / ln(1.03)

           n = 10.0062...

so a domain of 0 ≤ n ≤ 10 is reasonable

B) y-intercept is the height of the plant on day 0 which would be 12 cm

C) f(3) = 12(1.03)³ = 13.11 cm

average rate of change = Δh/Δn = (16.13 - 13.11) / (10 - 3) = 3.02 / 7

= 0.43 cm/day  or average growth per day