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

n

step-by-step explanation:

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.