Question

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) = 9(1.04)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 12.81 mm. What is a reasonable domain to plot the growth function? (4 points)

Answer 1

Answer:

A reasonable domain is $d = 9$ days

Step-by-step explanation:

Given:

The equation to show the growth of algae's radius is given as:

$f(d) = 9(1.04)^d$

Where, 'd' represents the number of days passed. So, it represents the domain of the given function $f(d)$.

$f(d)$ is the function representing the radius of algae after 'd' days.

Now, the radius of algae given after 'd' days = 12.81 mm

Therefore, plug in 12.81 for  $f(d)$. This gives,

$12.81=9(1.04)^d\\\\\frac{12.81}{9}=(1.04)^d\\\\\textrm{Taking log on both the sides, we get:}\\\\\log (\frac{12.81}{9})=\log(1.04)^d\\\\\textrm{Using log property} \log a^b=b\log a\\\\ \therefore \log (\frac{12.81}{9})=d\times\log(1.04)\\\\d=\frac{\log (\frac{12.81}{9})}{\log(1.04)}\\\\d=9\ days$

Therefore, after 9 days, the radius of algae is 12.81 mm.