Question

Is anybody doing buzz academy for your school program this year? Plz don't answer if you are not. And if you are, I need help with 4.12 part 2 in algebra.

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? (4 points)

Answer 1

9514 1404 393

Answer:

A) domain: 0 ≤ n ≤ 10

B) the height at the start of the study

C) 0.431 cm per day, average growth rate

Explanation:

A) The study started on day 0 and ended on day 10. A reasonable domain is ...

0 ≤ n ≤ 10

__

B) The y-intercept of the graph of plant height is the height of the plant on day 0, the day the study started.

__

C) On day 3, the height was ...

f(3) = 12·1.03^3 ≈ 13.1127 . . . cm

On day 10, it was ...

f(10) = 12·1.03^10 ≈ 16.1270 . . . cm

Then the plant grew at an average rate of ...

(16.1270 -13.1127) cm/(10 -3 days) ≈ 0.431 . . . cm/day

The average rate of change is the average rate of growth of the plant in the given period.