Question

Shelly is a biologist who wants to determine the growth rate of a strain of bacteriaShelly puts 85 bacteria into a controlled environment and waits 4 hours. When Shelly checks 4 hours later, there are 850 bacteria. What is the hourly growth rate of the bacteria?

Write your answer as a numeric value, such as: 345.59 Round your answer to the second decimal place.

Answer 1

The hourly growth rate is 0.58 (this is the rounded answer)

Explanation:

FORMULA: A = Pe^rt

Shelly is a biologist who wants to determine the growth rate of a strain of bacteria. Shelly puts 85 bacteria into a controlled environment and waits 4 hours. When Shelly checks 4 hours later, there are 850 bacteria. What is the hourly growth rate of the bacteria? Let A be the amount of bacteria at the end of the study and P be the amount of bacteria at the beginning of the study. Let r be the growth rate and t be the time it took for the bacteria to grow.

This being said,

850 = 85e^4r

r=0.58

Answer 2

The hourly growth rate of bacteria is 191.25

Solution:

Given that, initially Shelly put 85 bacteria and waits 4 hours

Amount of bacteria after 4 hours = 850

Now, number of bacteria increased = 850 bacteria – initial 85 bacteria

Number of increased bacteria = 850 – 85 = 765 bacteria.

So, 765 bacteria were produced in 4 hours.

So hourly growth rate( per hour) can be found out by as follows:

`\text { Hourly growth rate }=\frac{\text { number of bacteria increased }}{\text { number of hours }}`

`\text { Hourly growth rate }=(765)/(4)=191.25`

Hence, the hourly growth rate of bacteria is 191.25