Question

A scientist is studying the growth of anew species of bacteria. Looking back on his meticulous records, the scientist sees that his starting population was 50 bacteria. Five hours later, he measured 550 bacteria. What is the population of the bacteria after 10 hours, after 20 hours?

Answer 1

Explanation:

550 = 50
`x^(5)`

11 =
`x^(5)`

ln(11) = 5 ln(x)

x =
`e^(ln(11)/5)`

x = 1.615

10 hours ....

A= 50 (
`1.615^(10)` )

A= 50 (
`1.615^(10)` )

A=6050

20 hours ....

A= 50 (
`1.615^(20)` )

A= 50 (
`1.615^(20)` )

A=732,050

Answer 2

In 10 hours, the population is 6050 bacteria. In 20 hours, the population is 732050 bacteria.

Explanation:

Bacterial populations can be assumed to grow exponentially. In 5 hours, since the population will have multiplied by 11, in 10 hours it will have multiplied by 121 (11^2) and by 14641 (11^4).

50 * 11 * 11 = 6050

50 * 11 * 11 * 11 * 11 = 732050