A scientist is growing a colony of bacteria. Initially, the number of bacteria g

Question

A scientist is growing a colony of bacteria. Initially, the number of bacteria grows exponentially, but after many days, the colony stabilizes at 24000 bacteria. Suppose that t hours after the scientist begins, the number of bacteria, in thousands, can be modeled by the equation

B(t) = {0.2e0.315t 0 ? t ? 6 and (6t^2/at^b + c) for t > 6

Assuming that B is a continuous function of t, find the values of a, b, and c.

Consider the functions f(x) = sin(|x|x) and g(x) = (|x|)/ sin(?x)

(a) For each of the limits below, find an estimate of the limit or explain why the limit fails to exist. Be sure to include an explanation along with any graph or table that you use.

i. lim f (x) x?0+

ii. lim f (x) x?0?

iii. lim g(x) x?0+

iv. lim g(x) x?0?

(b) For each of the limits below, use your answers above to find an estimate of the limit or explain why the limit fails to exist.

i. limf(x) x?0

ii. limg(x) x?0

Explanation / Answer

1

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