Ascientist 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)

A) domain = [0, 5]

B) It represent the initial height of the plant, which was 10 cm.

C) It represent the average height increment of the plant between those days, which was 0.21 cm/day

Step-by-step explanation:

f(n) = 10*(1.02)^n

Part A

If the height is  11.04 cm, then:

11.04 = 10*(1.02)^n

1.104 = (1.02)^n

log(1.104) = n*log(1.02)

n = log(1.104)/log(1.02)

n = 5

The domain are all the possible n values; starting at day zero, the domain is [0, 5]

Part B

Replacing with n = 0 in the function we get:

f(0) = 10*(1.02)^0 = 10

It represent the initial height of the plant, which was 10 cm.

Part C

The average rate of change is the change of the function values divided by the change in the input values, that is:

average rate of change = ( f(5) - f(1) )/(5 - 1)

f(5) = 11.04

f(1) = 10*(1.02)^1 = 10.2

average rate of change = ( 11.04 - 10.2 )/4 = 0.21

It represent the average height increment of the plant between those days,  which was 0.21 cm/day

(2,9)

i think thats the answer i checked it on google

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b