On Novermber 27, 1993, the New York times reported that wildlife biologists have found a direct ink between the increase in the human population in florida and the decline of the local black bear population. From 1953 to 1993 the human population increased, on average, at a rate of 8% per year, while the black bear population decreased at a rate of 6% per year. In 1853 the black bear population was 11,000.

a) The 1993 human population of Florida was 13 million. What as the human population in 1953?
b) Find the black bear population for 1993.
c) If this trend continues, when will the black bear population number less than 100?

a.  1 263 888

b. 130 701

c. 72 years

Step-by-step explanation:

a. The differential equation applies here.

Let the quantity increase for a certain time be given by Q(t)

Every unity of time, the quantity increases by so that after the time t, the quantity remaining will be given by:

In a similar manner, the quantity R(t) decreases at a rate given by the following expression:

and after the time , t the quantity of R remaining will be given by:

a. To find the population of humans in 1953

1993 - 1953 = 40 years = t

Q(40) = Q×

Q = 1 263 888.44

    ≈ 1 263 888

b. For bear population in 1993:

t = 40

R(40) =

b = 130 700. 889

    ≈130 701

c. time taken for black bear population number less than 100 is given by:

130 = 11000×

solving using natural logarithms gives t = 72.72666

                                                                  =   72 years Ans

4153. Read the explanation please. There is no point in just reading the answer because the same type of problem can come up in the RSM homework or in a test and you will have no idea how to solve it.

Step-by-step explanation:

Form an equation with the information you know.

1. Moving the last digit, 3, to the first position is the same as doing (x-3)/10 +3000, where x is the original 4-digit number.

    Why it works: This expression works because first, you subtract 3 from the original number. This removes 3 from the last digit, but leaves a zero there. To remove the zero, you divide by 10. Finally, to put the 3 at the first position, you add 3000.

2. Since you know that the number will decrease by 738, you can do the second part of forming the equation. Make the expression equal to x - 738, like so --> (x-3)/10 + 3000 = x - 738

Solve the equation.

3. (x-3)/10 + 3000 = x-73

   (x-3)/10 = x - 3738

   x-3 = 10x - 37380

   x = 10x - 37377

   -9x = -37377

   x = 4153

Well, I've got to get back to my RSM homework. I hope this helped!

P.S.- The next time you have a question, email your RSM teacher (I'm assuming you go to RSM) because he/she is much more qualified then me (I'm only 12) and you don't really know if you can trust people giving you answers on