Physics, 11.03.2020 20:52 salutemeimchloe

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)

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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.

Answer from: Quest

tube or goog with be a great resource to with that question

Answer from: Quest

Iread this book last year so take this with a grain of salt.gene jumps from the tree to compete with finny due to the fact that gene is always trying to do better than finny. he is put under the grasp of peer pressure due to finny almost forcing him to do this. ever since he first jumped finny kept pressuring him to jump since he thought gene enjoyed jumping.rather than uses this answer you should probably just reread chapters 3-4

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