The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. after 3 hours it is observed that 500 bacteria are present. after 10 hours 4000 bacteria are present. what was the initial number of bacteria? (round your answer to the nearest integer.)

The initial number of bacteria is 371.

Explanation:

Let P represents population of the bacteria and t represents time,

According to the question,

Where, k is constant of proportionality,

Integrating both sides,

    ( Let )

If t = 0,

That is, is the intial population.

Since, when t = 3, P = 500 and when t = 10, P=4000

Hence, initial population is approximately 371.

try using substitution:

x + y - 6 = x - y. (i'm not giving you the exact answer). since 0 = x - y, then sub 0 in the equation with x - y. combine your like terms, and then use inverse operations, and you'll have your answer.

: -)