algebra - exponentials

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My question is how do I know that
N increases by a factor of 2.9 each day. (see below)

Let N(t) be number of bacteria after t days. N(t) = Pa^t for some constants P and a. N(2) = 5400 and N(6)=382,000.

a)before working problem, estimate value of N(5).

b) write down 2 equations for P and a, one when t=2 and one when t=6, and use these two equations to compute a and P. Round to three significant digits.

(a) N increases by a factor of 2.9 each day. Divide 382,000 by 2.9 for N(5)

(b) 382,000 P*a^6
5400 = P*a^2
70.74 - a^4
a = (70.74)^(1/4) = ___
Once you have a, solve for P.

• algebra - exponentials -

Because, as it shows above a = (70.74)^(1/4)= 2.9

and P*a^n multiples by a each day.

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