Answer:
The approximate difference in the growth rate of the two populations is 40%.
Step-by-step explanation:
The general exponential growth model is
[tex]y=a(1+r)^t[/tex]
Where, a is initial value, r is growth rate and t is time.
In the given graph, red curve passing through the points (2,22.5) and (3,33.75).
[tex]22.5=a(1+r)^2[/tex] .... (1)
[tex]33.75=a(1+r)^3[/tex] .... (2)
Divide the equation (2) by equation (1).
[tex]1.5=1+r[/tex]
[tex]0.5=r[/tex]
The graph rate of red curve is 50%.
In the given graph, purple curve passing through the points (7,19.4) and (8,21.4).
[tex]19.4=a(1+r)^7[/tex] .... (3)
[tex]21.4=a(1+r)^8[/tex] .... (4)
Divide the equation (4) by equation (3).
[tex]1.1031=1+r[/tex]
[tex]0.1031=r[/tex]
[tex]0.1\approx r[/tex]
The graph rate of red curve is 10%.
The approximate difference in the growth rate of the two populations is
[tex]50-10=40\%[/tex]
Therefore the approximate difference in the growth rate of the two populations is 40%.
