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ANSWER ASAPPP PLSSS. ILL MARK BRAINLIEST TOO



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? (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)

Respuesta :

saraalvi00

Answer:

Step-by-step explanation:

11.04 = 10(1.02)^n

1.104 = 1.02^n

ln 1.104 = ln 1.02^n

ln 1.104 = n ln 1.02

n = ln 1.104/ ln 1.02

n = 4.99630409516

4.99 can be rounded to 5.

So a reasonable domain would be 0 ≤ x < 5

PART B)

f(0) = 10(1.02)^0

f(0) = 10(1)

f(0) = 10

The y-intercept represents the height of the plant when they began the experiment.

f(1) = 10(1.02)^1

f(1) = 10(1.02)

f(1) = 10.2

(1, 10.2)

f(5) = 10(1.02)^5

f(5) = 10(1.1040808)

f(5) = 11.040808

f(1)=10(1.02)^1

f(1)=10.2

Average rate= (fn2-fn1)/(n2-n1)

                     =11.04-10.2/(5-1)

                    =0.22

the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

wegnerkolmp2741o

Answer:

Part A

The domain should be 0 ≤n≤5

Part B

f(n) = 10(1.02)^n

The function is in the form y =a b^x  where a is the y intercept

The y intercept is 10.  This is the value when n =0 days.

Part C

The average rate of growth over the 4 days is .21 cm per day

Step-by-step explanation:

f(n) = 10(1.02)^n

Part A

Let f(n) = 11.04

11.04 = 10 * 1.02 ^n

Divide each side by 10

11.04/10 = 1.02^n

1.104 = 1.02^n

Taking the log of each side

log 1.104 = log 1.02^n

We know log a^b = b log a

log 1.104 = n log 1.02

log 1.104 / log 1.02 = n

4.99630=n

Rounding n to 5

The domain should be 0 ≤n≤5

Part B

f(n) = 10(1.02)^n

The function is in the form y =a b^x  where a is the y intercept

The y intercept is 10.  This is the value when n =0 days.

Part C

To find the average rate of change

f(5) - f(1)

-----------

5-1

f(5) = 11.04  

f(1) = 10 *1.02 =10.2

11.04 - 10.2

-----------

5-1

.84

-----

4

.21 cm per day

The average rate of growth over the 4 days is .21 cm per day

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