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 centimeters after n days: F_N = 12(1.03)^n. When the scientist concluded his study, the height of the plant was approximately 16.13 cm.

What does the y-intercept of the graph of the function F_N represent?

A) The initial height of the plant when n = 0.
B) The average rate of change of the plant's height.
C) The final height of the plant when n = 16.13.
D) The growth rate of the plant over time.

Answer 1

The y-intercept of the function F_N = 12(1.03)^n represents the plant's initial height of 12 centimeters when n equals 0, which is answer A.

Step-by-step explanation:

The y-intercept of the graph of the given function F_N = 12(1.03)^n represents the initial height of the plant when n = 0. This is because when we set n to zero in the equation, the exponentiated part becomes 1 (1.03^0 = 1), leaving us with the coefficient 12, which is the height of the plant in centimeters at the start of the observation period. Therefore, the correct answer is A) The initial height of the plant when n = 0.

The growth rate of the plant over time is indicated by the base of the exponent, 1.03. This means that each day, the plant's height increases by 3% of its height from the previous day. This exponential model reflects the compounding nature of growth, where each day's growth builds upon the total size of the plant up to that day.