Mathematics, 10.12.2019 02:31, bks53

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?

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?

Answers: 2

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Answers

answered: ExclusiveNay

Part A) The reasonable domain for n is the interval [0,5]

Part B) The y-intercept is the height of the plant at the beginning of the study

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

Step-by-step explanation:

Part A)

we have

f(n)=10(1.02)^n

This is a exponential function of the form

f(n)=a(b)^n

where

f(n) is the height of the plant in cm

n is the number of days

a is the initial value or y-intercept of the function

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 (value of he function when the value of n is equal to zero)

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

For f(n)=11.04 cm ----> Find the value of n

11.04=10(1.02)^n

1.104=(1.02)^n

Apply log both sides

log(1.104)=n[log(1.02)]

Solve for n

$n=5\ days$

therefore

The reasonable domain for n is the interval [0,5]

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

we know that

The y-intercept or initial value of the function is equal to 10 cm

Remember that the y-intercept is the value of the function f(n) when the value of n is equal to zero

In this context the y-intercept is the height of the plant at the beginning of the study

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?

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

answered: Guest

step-by-step explanation:

you are throwing one dart

answered: Guest

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

$\tan\left(x\right)=\frac{\left[altitude\right]}{\left[base\right]}=\frac{p}{r}$