Bob 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

Question

1. Starting from 0 days, plug x-values into our function to find out how many days it takes for the plant to grow to 11.04 cm

2. Write a compound inequality to show the reasonable domain of the plant growth:
my answer: f(n) = 10(1.02)n

3. What is the y-intercept of our function?
My answer: The height of the plant

4. What does the y-intercept of the graph of the function f(n) represent?

My Answer: i'm stuck
5. What is the average rate of change formula for exponential growth functions?
My Answer:???

6. Plug and chug n= 1 to n = 5 into your formula above. Show all work!
My Answer: f(n) = 10(1.02)n 11.04=10(1.02)5

7. What does the average rate of change answer represent?
My Answer: Growth per day.

Answer 1

11.04 = 10 (1.02)^n
I am not going to try lots of days, boring
log 11.04 = log 10 + n log 1.02
4.996 days
so five days

2. n>0 and <the life of the plant

3. when n = 0, height = 10

4. the height of the plant when we bought it

5. F(n+1) = F(n) * 1.02

6. calculate F(1) = 10(1.02) = 10.2
then F(2) = 10.2 * 1.02 =
F(3) = F(2) * 1.02 = etc

7. ratio of next day height to previous day height

Answer 2

OMG, I thought I knew this stuff better!!

Now i'm really lost!!

Answer 3

I guess I did not explain very well

in the first question for example it asks you to plug and chug from 0 to 11.04

I did not bother but
first day
10*1.02 = 10.2
second day
10.2 * 1.02 = 10.4
third day
10.4 * 1.02 = 10.61
fourth day
10.61 * 1.02 = etc until you get to 11.04

Answer 4

10.82
fifth day
10.82*1.02 = 11.04 done

Answer 5

Is # 6 like this
F(1)= 10(1.02) = 10.2
F(2)= 10.2 x 1.02 = 10.40
F(3=10.404 x 1.02 = 10.61
then continue? So, the final answer is 11.04?

Answer 6

Yes, it told you to keep doing it until you get to 11.04, that was after 5 days
(I cheated and took the log of both sides so solve directly)

Answer 7

I believe 1 and 6 are the same question asked different ways.

Answer 8

The important thing here is that the rate of change is proportional to your present value, so the change keeps changing.
The most common example is compound interest

Answer 9

if interest rate is 2% per year compounded yearly
then

Yn+1 = Yn + .02 Yn = Yn (1.02)

and in general
Y = Yinitial * (1.02)^n