Answer:
The approximate difference in the growth rate of the two populations is 40%.
Step-by-step explanation:
The complete question is
The graph shows the population of deer for the past 5 years. what is the approximate difference in the growth rate of the two populations?
The picture of the question in the attached figure
we know that
The equation of a exponential growth function is given by
[tex]y=a(1+r)^x[/tex]
where
y is the population
x is the number of years
a is the initial value
r is the growth rate
step 1
Find the equation of the red curve
we have
[tex]a=10[/tex] ---> value of y when the value of x is equal to zero
substitute
[tex]y=10(1+r)^x[/tex]
we have the point (2,22.5)
substitute the value of x and the value of y in the equation
[tex]22.5=10(1+r)^2[/tex]
solve for r
[tex]2.25=(1+r)^2[/tex]
square root both sides
[tex]1+r=1.5\\r=1.5-1\\r=0.5[/tex]
therefore
The growth rate of red curve is 0.50 or 50%
step 2
Find the equation of the blue curve
we have
[tex]a=10[/tex] ---> value of y when the value of x is equal to zero
substitute
[tex]y=10(1+r)^x[/tex]
we have the point (7,19.4)
substitute the value of x and the value of y in the equation
[tex]19.4=10(1+r)^7[/tex]
solve for r
[tex]1.94=(1+r)^7[/tex]
elevated both side to 1/7
[tex]1+r=\sqrt[7]{1.94}[/tex]
[tex]r=1.10-1\\r=0.10[/tex]
therefore
The growth rate of red curve is 0.10 or 10%
step 3
Find the approximate difference in the growth rate of the two populations
Subtract the two growth rate
[tex]50-10=40\%[/tex]
Therefore
The approximate difference in the growth rate of the two populations is 40%.
