Mathematics, 28.11.2019 05:31 patrickfutrell2537

Asap 100pts part a and part b
dont copy others i can tell and report you

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 is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?

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Answer from: dhhdndnd

Part A) The reasonable domain to plot the growth function is the interval [0,5]

Part B) The average rate of change is $0.21\ \frac{cm}{day}$

see the explanation

Step-by-step explanation:

Part A)

Let

f(n) -----> the height of the plant in cm

n ----> the number of days

we have

f(n)=10(1.02)^n

This is a exponential function of the form

f(x)=a(b)^x

where

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

In this problem we have

$a=10\ cm$ ----> initial value or y-intercept

$b=1.02\\r=b-1=1.02-1=0.02\\r=2\%$

For f(n)=11.04 cm

Find the value of n

substitute in the exponential function

$11.04=10(1.02)^n\\11.04/10=(1.02)^n\\1.104=(1.02)^n$

Apply log both sides

$log(1.104)=(n)log(1.02)\\n=log(1.104)/log(1.02)\\n=5\ days$

The reasonable domain to plot the growth function is the interval -----> [0,5]

$0 \leq x \leq 5$

Part B) What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?

the average rate of change is equal to

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

$f(a)=f(1)=10(1.02)^1=10.2\ cm f(b)=f(5)=10(1.02)^5=11.04\ cm\\a=1\\b=5\\$

Substitute

$\frac{11.04-10.2}{5-1}=0.21\ \frac{cm}{day}$

The average rate of change is the change of the function values (output values) divided by the change of the input values.

That represent ----> The plant grew an average of 0.21 cm per day during that time interval

Answer from: Quest

Wow. that is a really cool question.

Answer from: Quest

Hello!

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

why?

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

$3x-6$

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

$3x-6=0$

$3x=6$

$x=\frac{6}{3}=2$

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

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Asap 100pts part a and part b
dont copy others i can tell and report you

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