1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
NikAS [45]
2 years ago
12

A biologist is studying the growth of a particular species of algae. She writes the fall inclusion to show the radius of the alg

ae, f(d), in mm, after d days: f(d)=5(1.02)^d
Part A- When the biologist concluded her study, the radius of the algae was approximately 6.34mm. What is a reasonable domain to plot the growth function

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

Part C- what is the average rate of change of the the function f(d) from d=4 to d=11, and what does it represent?
Mathematics
1 answer:
horrorfan [7]2 years ago
5 0

Answer:

Part A)

A reasonable domain to plot the growth function is:

0\leq d \leq 12

Part B)

The <em>y-</em>intercept represents that when the biologist started her study, the radius of the algae was five millimeters.

Part C)

The average rate of change from <em>d</em> = 4 to <em>d</em> = 11 was about 0.11. This means that from the 4th day to the 11th, the radius of the algae grew, on average, at a rate of 0.11 mm per day.

Step-by-step explanation:

The radius of the algae f(d) in millimeters after <em>d</em> days is given by the function:

f(d)=5(1.02)^d

Part A)

We know that the radius of the algae was approximately 6.34 mm when the biologist concluded her study. To find the reasonable domain, we can substitute 6.34 for f(d) and solve for <em>d</em>. Therefore:

6.34=5(1.02)^d

Divide both sides by five:

(1.02)^d=1.268

Take the log of both sides with base 1.02:

\displaystyle d=\log_{1.02}1.268

Using the Change of Base Property, evaluate for <em>d: </em>

<em />\displaystyle d=\frac{\log 1.268}{\log 1.02}=11.9903...\approx 12<em />

So, the biologist concluded her study after 12 days.

Therefore, a reasonable domain to plot the growth function is:

0\leq d\leq 12

Part 2)

The <em>y-</em>intercept of the function is when <em>d</em> = 0. Find the <em>y-</em>intercept:

f(0)=5(1.02)^{(0)}=5(1)=5

Since <em>d</em> represent the amount of days after the study had begun, the <em>y-</em>intercept represents the radius of the algae on the initial day.

So, when the biologist started her study, the radius of the algae was five millimeters.

Part 3)

To find the average rate of change for a nonlinear function, we find the slope between the two endpoints on the interval.

We want to find the average rate of change of f(d) from <em>d</em> = 4 to <em>d</em> = 11.

Find the endpoints:

f(4)=5.4121...\text{ and } f(11)=6.2168...

And find the slope between them:

\displaystyle m=\frac{f(11)-f(4)}{11-4}=0.1149...\approx 0.11

Since f(d) measures millimeters and <em>d</em> measures days, this tells us that, on average, the radius of the algae grew by about 0.11 mm per day from the 4th day to the 11th day.

You might be interested in
Please help me please
spayn [35]

Answer:

A. 34°

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Trigonometry</u>

  • [Right Triangles Only] SOHCAHTOA
  • [Right Triangles Only] tanθ = opposite over adjacent
  • Inverse Trig

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

Angle θ = <em>x</em>

Opposite leg AC = 24

Adjacent leg CB = 35

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Substitute in variables [Tangent]:                                                                    \displaystyle tanx^\circ = \frac{24}{35}
  2. Inverse Trig [Tangent]:                                                                                     \displaystyle x^\circ = tan^{-1}(\frac{24}{35})
  3. Evaluate:                                                                                                           \displaystyle x = 34.439^\circ
  4. Round:                                                                                                               \displaystyle x \approx 34^\circ
4 0
2 years ago
Harry buys 3 granola bars for $5. Sidnee buys
juin [17]

Answer:

The constant of proportionality is 5/3

Step-by-step explanation:

3 * k = 5

k = 5/3

Check

9 * k = 15

9 * 5/3 = 15

3*5 = 15

15 =15

The constant of proportionality is 5/3

3 0
2 years ago
Read 2 more answers
PLEASE HELP!!! I need the answer and the work to go along with it.
Masja [62]
----------------------------------------------------------------------------------------------------
Check the picture attached.

the secants of the circle, BA and DC, intersect at point P, as shown.

i)
let m(P)=a

ii)
let m(CDA)=b, then the measure of ar CA is 2b, as "the measure of an inscribed angle is half the measure of the arc it intercepts"

iii)
m(DAB)= m(P)+m(CDA)= a+b, as DAB is an exterior angle of the triangle PAD.

iv)
then the measure of arc DB is 2m(DAB)=2(a+b)=2a+2b

v)
m(P)= \frac{(2a+2b)-2b}{2}= \frac{m(DB)-m(CA)}{2}

This is always true,
----------------------------------------------------------------------------------------------------

In our problem, there is a slight difference, we have 1 secant and one tangent, but it is just a special case and nothing changes.

As an exercise, we can repeat the steps of the general proof, by first joining U and T.
----------------------------------------------------------------------------------------------------

by the theorem we just proved,

m(R)=(m(TU)-m(SU))/2

30°=(100°-m(SU))/2

60°=100°-m(SU)

m(SU)=40°

5 0
2 years ago
Select the correct answer.
AlladinOne [14]

Answer:

A or D

Step-by-step explanation:

i did this on khan academy thats why ;)

3 0
2 years ago
Read 2 more answers
Confidence Intervals for Curved Gaussian Family Bookmark this page (a) 1 point possible (graded) Let X1,…,Xn be i.i.d. random va
Nostrana [21]

Answer:

True

True

Step-by-step explanation:

The unknown parameters are treated as variable and data serve as coefficients. The random variables are value whose outcome depends on some random event. The θ can exist when n ≥ 0. A sample mean is a sequence which has normal distribution and n ≥ 1. The sample average of X-n follows normal distribution for all integer and n is greater or equal to 1.

7 0
3 years ago
Other questions:
  • HELP 25pts and will mark brainliest. I NEED THIS NOW!! Which expression shows the result of applying the distributive property t
    9·1 answer
  • 8a + 16<img src="https://tex.z-dn.net/?f=8a%20%2B%2016" id="TexFormula1" title="8a + 16" alt="8a + 16" align="absmiddle" class="
    5·1 answer
  • Sketch the region enclosed by y=e3x,y=e5x and x=1. Decide whether to integrate with respect to x or y, and then find the area of
    13·1 answer
  • 61 ones×<br> ​10<br> ​<br> ​1<br> ​​ = ?
    8·2 answers
  • The price of a shirt is usually £45. During a sale the prices in the shop are reduced by 2 5 . How much is the shirt in the sale
    8·1 answer
  • The perimeter of a rectangular garden is 62 feet( remember, perimeter= 2l + 2w where l is the length and w is the width). The le
    9·1 answer
  • martin reads 19 pages of a novel in 12 minutes. complete the proportion and use it to find x, the number of pages he reads in 42
    6·1 answer
  • If RG = 4X+12 and HI = 10x-15, then x =​
    5·1 answer
  • I'm depressed and bored can anyone talk but pls pls no harmful talk pls a request ​
    15·1 answer
  • Which expression is equivalent €2x5/18? Assume x&gt;0.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!