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

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?

Answer 1

Answer:

The reasonable domain to plot the growth function is the interval [0,9]

$0\ days\leq d\leq 9\ days$

Step-by-step explanation:

In this problem we have a exponential function of the form

$f(d)=a(b^d)$

where

f(d) is the radius of the algae in mm

d is the number of days

a is the initial value or y-intercept

b is the base

r is the rate of growth

b=1+r

we have

$a=9\ mm\\b=1.04\\r=1.04-1=0.04=4\%$

we have

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

For f(d)=12.81 mm

substitute in the function and solve for d

$12.81=9(1.04^d)$

$(12.81/9)=(1.04^d)$

Apply log both sides

$log(12.81/9)=log(1.04^d)$

$log(12.81/9)=(d)log(1.04)$

$d=log(12.81/9)/log(1.04)$

$d=9\ days$

therefore

The reasonable domain to plot the growth function is the interval [0,9]

$0\ days\leq d\leq 9\ days$