Question

A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 3 hours there will be 780 bacteria.

(a) Express the population after t hours as a function of t.
population: ? (function of t)

(b) What will be the population after 3 hours?

(c) How long will it take for the population to reach 1870 ?

Answer 1

The solutions to the exponential growth problem are:

A. $P(t) = 260e^0.3662t$

B.$P(3) = 260e^0.3662(3) = 779$

C.3.367 hours

What is the formular for the exponential growth problem?

The  exponential growth problem obeys the equation:

P(t) = P0ekt

P0=population

time t

We can find the value of k At t=3 hours as,

780 = 260e^k(3)

k = (1/3) ln(780/260) hours-1 ≅ 0.3662 hours-1

A. $P(t) = 260e^0.3662t$

B. $P(3) = 260e^0.3662(3) = 779$

C.  1870 = 260e^0.3662t

To Solve for t, w2e make t the subject of the formula

t = ln(1870/260) / 0.3662 hours = 3.367 hours

Learn more about  exponential growth on:

https://brainly.com/question/27161222

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