# Calculus

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
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?
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.
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.

1. 👍
2. 👎
3. 👁

## Similar Questions

1. ### Algebra

The function y = –0.296x^2 + 2.7x models the length x and height y that your sister's pet rabbit can jump, in centimeters. How high does the rabbit jump? One the rabbit reaches the ground what is the total length of the jump? I

2. ### Physics

Starting from a location with position vector 𝑟1,𝑥=−17.5 m and 𝑟1,𝑦=23.1 m , a rabbit hops around for 10.7 seconds with average velocity 𝑣𝑎𝑣,𝑥=−2.25 m/s and 𝑣𝑎𝑣,𝑦=1.79 m/s . Find the

3. ### math

a rabbit climb up a flight of 10 stairs and can only hop 1 or 2 steps each time. he never hops down, only up. How many ways can the rabbit hop up the flight of 10 steps?

4. ### Science help (just 4 questions)

1. Which of the following is an example of an environmental pressure? (1 point) the air pressure in the atmosphere a lake that is gradually running out of water a fight between two members of the same species breeding between two

1. ### Physics

A rabbit can cover a distance of 80 m in 5 s. What is the speed of the rabbit?

2. ### Physics

Show that the average speed of a rabbit that runs a distance of 30 m in a time of 2 s is 15 m/s. I have a whole bunch of problems such as these and i'm not sure what math formula to use to figure problem.I know its Acceleration !

3. ### Biology

1. Two species live in the same area but breed in different parts of their habitat. These species are A) geographically isolated. B) ecologically isolated. C) artificially isolated. D) likely to produce hybrids. 2. A large

4. ### Mathematics

It has been observed that a particular plant's growth is directly proportional to time. It measured 2 cm when it arrived at the nursery and grows at a rate of .5 cm per week this is represented with the function g(x)= 2+ .5x where

1. ### calculus

The rabbit population on a small island is observed to be given by the function P(t)=120t−0.4t4+700 where t is the time (in months) since observations of the island began.

2. ### Maths

Mother rabbit hops 8steps at a time while baby rabbit hops 4steps at a time. which steps will they both hop on? Draw on the number line to find out. ​

3. ### Physics

A rabbit runs in a garden such that the x- and y-components of its displacement as function of times are given by x(t) = −0.44t2 − 6.0t + 73 and y(t)= 0.35t2 + 8.3t + 34. (Both x and y are in meters and t is in seconds.) (a)

4. ### Physics

Two cars, A and B, travel in a straight line. The distance of A from the starting point is given as a function of time by xA(t)=αt+βt^2, with α=2.60m/s and β=1.20m/s^2. The distance of B from the starting point is