Answer:
The approximate difference in the growth rate of the two populations is 40%.
Step-by-step explanation:
<u><em>The complete question is</em></u>
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
![y=a(1+r)^x](https://tex.z-dn.net/?f=y%3Da%281%2Br%29%5Ex)
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
---> value of y when the value of x is equal to zero
substitute
![y=10(1+r)^x](https://tex.z-dn.net/?f=y%3D10%281%2Br%29%5Ex)
we have the point (2,22.5)
substitute the value of x and the value of y in the equation
![22.5=10(1+r)^2](https://tex.z-dn.net/?f=22.5%3D10%281%2Br%29%5E2)
solve for r
![2.25=(1+r)^2](https://tex.z-dn.net/?f=2.25%3D%281%2Br%29%5E2)
square root both sides
![1+r=1.5\\r=1.5-1\\r=0.5](https://tex.z-dn.net/?f=1%2Br%3D1.5%5C%5Cr%3D1.5-1%5C%5Cr%3D0.5)
therefore
The growth rate of red curve is 0.50 or 50%
step 2
Find the equation of the blue curve
we have
---> value of y when the value of x is equal to zero
substitute
![y=10(1+r)^x](https://tex.z-dn.net/?f=y%3D10%281%2Br%29%5Ex)
we have the point (7,19.4)
substitute the value of x and the value of y in the equation
![19.4=10(1+r)^7](https://tex.z-dn.net/?f=19.4%3D10%281%2Br%29%5E7)
solve for r
![1.94=(1+r)^7](https://tex.z-dn.net/?f=1.94%3D%281%2Br%29%5E7)
elevated both side to 1/7
![1+r=\sqrt[7]{1.94}](https://tex.z-dn.net/?f=1%2Br%3D%5Csqrt%5B7%5D%7B1.94%7D)
![r=1.10-1\\r=0.10](https://tex.z-dn.net/?f=r%3D1.10-1%5C%5Cr%3D0.10)
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
![50-10=40\%](https://tex.z-dn.net/?f=50-10%3D40%5C%25)
Therefore
The approximate difference in the growth rate of the two populations is 40%.