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

since the airplane is moving with constant speed then the distance travelled can be calculated by x=u*t

in km/h would be:

x=640*3.5=2.240 km

in m/s would be:

u=640 km/h= 640.000 m/h =640.000/ 3600 m/s =177.8 m/s

t= 3.5 h= 3.5 * 3600 s=12.600 s

then x=u*t= 177.8*12.600= 2.240.280 m

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step-by-step explanation: