Question

A bacteria culture starts with 580 bacteria and grows at a rate proportional to its size. After 3 hours there will be 1740 bacteria.

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

Answer 1

The population after t hours can be expressed as: P(t) = 580 * e^((ln(3)/3)*t)

Step-by-step explanation:

To express the population after t hours as a function of t, we can use the formula for exponential growth.

The formula is given by P(t) = P(0) * e^(kt), where P(t) is the population after t hours, P(0) is the initial population, k is the growth rate constant, and e is Euler's number (approximately 2.71828).

In this case, the initial population is 580 and after 3 hours, the population is 1740. Using these values, we can solve for k:

1740 = 580 * e^(3k)

Dividing both sides by 580 gives:

3 = e^(3k)

Taking the natural logarithm of both sides gives:

ln(3) = 3k

Dividing both sides by 3 gives:

k = ln(3)/3

Therefore, the population after t hours can be expressed as:

P(t) = 580 * e^((ln(3)/3)*t)