Question

ANSWER ASAP PLS!!!!!

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) = 10(1.02)n

Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 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 = 1 to n = 5, and what does it represent? (4 points)

Answer 1

Answer:

see below

Step-by-step explanation:

f(n) = 10(1.02)^n

Part A

Let f(n) = 11.04

11.04 = 10 * 1.02 ^n

Divide each side by 10

11.04/10 = 1.02^n

1.104 = 1.02^n

Taking the log of each side

log 1.104 = log 1.02^n

We know log a^b = b log a

log 1.104 = n log 1.02

log 1.104 / log 1.02 = n

4.99630=n

Rounding n to 5

The domain should be 0 ≤n≤5

Part B

f(n) = 10(1.02)^n

The function is in the form y =a b^x  where a is the y intercept

The y intercept is 10.  This is the value when n =0 days.

Part C

To find the average rate of change

f(5) - f(1)

-----------

5-1

f(5) = 11.04  

f(1) = 10 *1.02 =10.2

11.04 - 10.2

-----------

5-1

.84

-----

4

.21 cm per day

The average rate of growth over the 4 days is .21 cm per day

Answer 2

Answer:

Part A: A reasonable domain to plot the growth of the function would be: 0 < n < 5.

Part B: The y-intercept of the graph of the function f(n) represents the height of the plant in 0 days when it first began.

Part C: The average rate of change of the function from n = 1 to n = 5 is 0.84 or 0.21cm per day. It represents the amount of growth for the plant over 4 days.

, Hope this helps :)

Have a great day!!