Question

General Mathematics:

Consider a population of bacteria that grows according to the function f(t) = 500e ^ (0.05t) , where t is measured in minutes. How many bacteria are present in the population after 4 hours?​

Answer 1

Given that:

• A population of bacteria that grows according to the function f(t) = 500e^(0.05t).
• Where t is measured in minutes.

To Find:

• How many bacteria are present in the population after 4 hours?

We know that:

• 1 hour = 60 minutes
• 4 hours = 4 × 60 = 240 minutes

The value of e = 2.71828182845

Finding the number of bacteria present:

↠ f(240) = 500 × e^(0.05 × 240)

↠ f(240) = 500 × e^12

↠ f(240) = 500 × 162754.791

↠ f(240) = 81377396

Hence,

• 81377396 bacteria are present in the population after 4 hours.

Answer 2

The population of bacteria after 4 hours will be 81377396.

Given,

The growth of population is according to the function f(t) = 500e^(0.05t).

To Find,

The number of bacteria present in the population after 4 hours.

Solution,

The given function is f(t) = 500e^(0.05t).

We will convert the time into minutes.

So,

1 hour = 60 minutes

4 hours = 4 × 60 = 240 minutes

The value of e = 2.71828182845

Now,  the number of bacteria present are

f(240) = 500 × e^(0.05 × 240)

f(240) = 500 × e^12

f(240) = 500 × 162754.791

f(240) = 81377396

Hence, 81377396 bacteria are present in the population after 4 hours.