Two separate rabbit populations are observed for 80 weeks, starting at the same time
and with the same initial populations. The growth rates of two rabbit populations are
modeled as follows, where t =0 corresponds to the beginning of the observation period:
r1(t)=4sin((2pi/72)(t)) +.1t+1, where r(1) is rabbits/week, t is time in weeks
r2(t)=t^(1/2) , where r (2) is rabbits per week, t is time in weeks
a. Using your calculator, find (approximately) the first positive time t for which the rates of
growth for the two populations are the same
-I assumed this meant where the two equations intersect. So 31.7 weeks.
b. What’s the physical significance of the area between the two curves from time t = 0 until
the first time where the two rates are the same? What does the area represent?
-That R(1) has a faster growth rate. Number of rabbits in population.
c. Suppose you want to find the first time (call it T) after the beginning of the observation
period at which the two rabbit populations have identical populations. Write an equation to
solve for the unknown variable T.
I really lost and not sure how this relates to definite integrals, and this makes my answers for a and b wrong.
d.Simplify your equation from part C until you can use your calculator on it. Then use your
calculator to solve this equation for T.
Any help especially on part c. and d. would be appreciated. thanks.
and with the same initial populations. The growth rates of two rabbit populations are
modeled as follows, where t =0 corresponds to the beginning of the observation period:
r1(t)=4sin((2pi/72)(t)) +.1t+1, where r(1) is rabbits/week, t is time in weeks
r2(t)=t^(1/2) , where r (2) is rabbits per week, t is time in weeks
a. Using your calculator, find (approximately) the first positive time t for which the rates of
growth for the two populations are the same
-I assumed this meant where the two equations intersect. So 31.7 weeks.
b. What’s the physical significance of the area between the two curves from time t = 0 until
the first time where the two rates are the same? What does the area represent?
-That R(1) has a faster growth rate. Number of rabbits in population.
c. Suppose you want to find the first time (call it T) after the beginning of the observation
period at which the two rabbit populations have identical populations. Write an equation to
solve for the unknown variable T.
I really lost and not sure how this relates to definite integrals, and this makes my answers for a and b wrong.
d.Simplify your equation from part C until you can use your calculator on it. Then use your
calculator to solve this equation for T.
Any help especially on part c. and d. would be appreciated. thanks.