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 17:20

Select a graph that have an equation with a < 0

Answers: 2

Answer

Mathematics, 21.06.2019 22:40

Suppose you are choosing a 6-digit personal access code. this code is made up of 4 digits chosen from 1 to 9, followed by 2 letters chosen from a to z. any of these digits or letters can be repeated. find the total number of personal access codes that can be formed. 492,804 341,172 39,917,124 4,435,236

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

Luis has a cooler filled with cans of soda.for every 5 cans of coke there are 3 cans of sprite.if there are 25 cans of coke, how mant cans of sprite are there?

Answers: 2

Answer

Mathematics, 22.06.2019 03:30

Lisette takes an ela exam and got 16 out of 27 questions correct. what percentage of the questions did lisette get correct?

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