Question

Math Check please!

Answer 1

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?

Part B: What does the y-intercept of the graph of the function f(n) represent?

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?

Answer 2

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? Since f(n) represents the plant height, as does 11.04 cm, equate these two and solve the resulting equation for n. Rounding this n up to the nearest integer would give you the upper endpoint of the domain. What would the lower endpoint be?

Answer 3

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?

Answer: Y = 10(1.02) ^ N = Y = 10.2 N = 11.04
11.04 = 10.02 N = 1.08235 = N
So, the domain is the number of days, so the number of days would be 0 to 2.

Part B: What does the y-intercept of the graph of the function f(n) represent?

Answer: What the Y-intercept represents is the height of the plant at the start of the experiment.

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?

Answer: What the rate of change is the slope of the line from the points ( 1, 10.2) to ( 5, 51 )
We can get the Y coordinate by plugging in the n values 1 and 5.

51 - 10.2 40.8 So, what this number represents
----------------- = --------- = 10.2 is the average amount of growth
5 -1 4 per day for the plant.

Answer 4

Are you sure that the last question is connected to the rest (i. e., to A and B)? We are told that the plant reaches the height 11.4 cm, a lot shorter than 11.4 cm. What's your own interpretation? You've concluded that the domain, in Part A, is between 1 and 2, but in part C it appears that n ranges from 0 to 5 days.

Answer 5

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?

Answer 6

I have a problem with your approach to Part A:

Answer: Y = 10(1.02) ^ N = Y = 10.2 N = 11.04
11.04 = 10.02 N = 1.08235 = N
So, the domain is the number of days, so the number of days would be 0 to 2.

From where does your "10.2 N" come from? Recall "order of operations" rules. Exponentiation takes place before multiplication.

Answer 7

While I can easily guess your meaning when you type in f(n) = 10(1.02)n, it'd be clearer and a lot more appropriate were you to type it as\[f(n)=10(1.02)^n\]

Answer 8

yeah, I probably should. Thanks for the help!

Answer 9

Alternatively, draw this expression:

Answer 10

You begin with f(n) = 10(1.02)n, better written as \[f(n)=10(1.02)^n\] and set that equal to 11.4 (cm). Would you please do that now, showing all steps of your solution for n.

Answer 11

\[0 \le y \le 2 \]

Answer 12

\[y = 10 ( 1.02) n\]

Answer 13

it can be rewritten as \[Y = 10.2 n\]

Answer 14

which then equals 11.04

Answer 15

Then 11.04 = 10.2n

Answer 16

\[11.04 \div 10.2 = n\]

Answer 17

Unfortunately, that is not the case. This assumption is the reason you're having some difficulty.
\[11.4=10(1.02)^n\]

Order of operations rules require that you do exponentiation first. You have done multiplication first: 10(1.02). NO.

Answer 18

Your job is to solve
\[11.4=10(1.02)^n \] for n. Do not multiply 1.02 by 10.

Answer 19

Hint: I found a value for n using logarithms.

Answer 20

Please find n.