Mathematics, 26.05.2020 19:58 gabrielaperezcz

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)
Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. 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(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent? (4 points)

Answers: 3

Show answers

Answers

Answer from: mothertrucker2828

A) The reasonalbe domain to plot the graph is 0 ≤ d ≤ 11 (days)

B) The y-intercept of the graph of the function f(d) represents the radius of the algae when the biologist started her study

C) The average rate from d = 4 to d = 11 is:

$\overline {Rate}=0.6358mm/day$

It represents that the radius of the algae increased an average of 0.6358mm per day from the fourth day until the last day of her study.

Explanation:

Start writting the equation properly

f(d)=7(1.06)^d

Where f(d) is in mm, and d is number of days.

Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. What is a reasonable domain to plot the growth function?

The domain should be the whole numbers since the moment the study starts (d = 0) up to the moment the biologist concluded her study.

To determine the number of days elapsed, you solve the equation for d and find it when f(d) is 13.29mm

$13.29=7(1.06)^d\\\\(1.06)^d=13.29/7\\\\d\log 1.06=\log (13.29/7)\\\\d=\dfrac{\log (13.29/7)}{\log 1.06}\\ \\ \\ d=11.00=11$

Therefore, the domain is 0 ≤ d ≤ 11 (days)

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

The y-intercept of a function is the value of the function for which its graph intercepts the vertical axis.

That happens when the independent variable, d in this case, is equal to zero: f(0).

d = 0 represents the moment when the biologist started her study, meaning that f(0) is the radius of the algae when the study started

To find the y-intercept you make d = 0 in the equation and fin find f(0)

That is:

$f(0)=7(1.06)^0=7\times 1=7$

Then, the y-intercept, the radius of the algae when the biologist started her study, is 7 mm.

Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent?

The average rate of change of the function f(d) from d = 4 to d = 11 is:

$\overline {Rate}=\dfrac{f(11)-f(4)}{11-4}$

$\overline {Rate}=\dfrac{7\cdot(1.06)^{11}-7\cdot (1.06)^4}{11-4}$

$\overline {Rate}=0.6358mm/day$

That means that the radius of the algae increased an average of 0.6358mm per day from the fourth day until the last day of the study.

Another question on Mathematics

Mathematics, 21.06.2019 14:30

F(x)= 1/x-4, g(x)=4x+1/x a. use composition to prove whether or not the functions are inverses of each other. b. express the domain of the compositions using interval notation.

Answers: 2

Answer

Mathematics, 21.06.2019 17:50

Segment ab is shown on the graph. which shows how to find the x-coordinate of the point that will divide ab into a 2: 3 ratio using the formula

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

3.17 scores on stats final. below are final exam scores of 20 introductory statistics students. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94 (a) the mean score is 77.7 points. with a standard deviation of 8.44 points. use this information to determine if the scores approximately follow the 68-95-99.7% rule. (b) do these data appear to follow a normal distribution? explain your reasoning using the graphs provided below.

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

Bella want to know what the students at her school think of her show. which is the best group to survey to find this information a. go to the mall and ask all of the students she recognizes from school b. ask her viewers to call in durning an episode of the show c. get a list of students at her school from the office and use a random number generator to pick 30 of them d. get a list of students at her school from the office and pick the first 30 students on the list

Answers: 1

Answer

You know the right answer?

A biologist is studying the growth of a particular species of algae. She writes the following equati...

Questions

Mathematics, 20.11.2020 03:50

Can somebody me with this thanks ...

Mathematics, 20.11.2020 03:50

-4x-3y =8 —3x+2y=-11 Miguel multiplies the top equation by 4 and the bottom equation by 3. Jenny says she would multiply the top equation by 2...