Math Is Fun Forum

ChrisB

Guest

Struggling with algebra quesion

Sometimes cats and their owners may suffer from an infestation of fleas.  A possible model for this annoying process is

            P(t) = A(1 – Be-kt)

    Where P(t) represents the number of fleas at time t (measured in days) while A, B and k are constants.  At the beginning of the summer one cat was host to 5 fleas and over the ensuing weeks (i.e. as t → ∞) these bred to a sustainable maximum of 1000 fleas.

    (a)    Use this data to show that A = 1000 and B = 0.995   

(b)    Determine the value of k to 2 decimal places knowing that after 1 week the cat had 250 fleas.                   

(c)    After how many days are there at least 900 fleas.  Give your answer correct to the nearest day.   

Really struggling with this, can anyone help?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,163

Re: Struggling with algebra quesion

hi ChrisB

Firstly, have a look at the exponential graph with negative exponent:

http://www.mathsisfun.com/data/function … nc1=e^(-x)

From this you can see what would happen to the Be^(-kt) term as t tends to infinity.

That will give you the value of A.

And setting t = 0 will give you the value of B

Then you can put t = 7 and using the values of A and B, you will be able to get k.

Finally you can put P = 900 and solve for t.

Hope that helps.  If you post back your answers I'll check them for you.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob