Question

The equation to model Exponential Growth is: y=a(1+r)t y= total amount a= starting amount r= the growth rate as a decimal t= number of growth periods Question 4 A sample of bacteria cells in a petri dish increases by 50% every hour. A scientist starts with a sample of 30 bacteria cells. Write an equation that can be used to determine the number of cells after x hours.

Answer 1

`y=30(1.5)^x`

where:

• y = total amount of bacteria cells
• x = number of hours

Explanation:

Given exponential growth equation:

`y=a(1+r)^t`

where:

• y = total amount
• a = starting amount
• r = the growth rate as a decimal
• t = number of growth periods

If a sample of bacteria cells in a petri dish increases by 50% every hour, the growth rate is:

• r = 50% = 0.5

If the starting amount of bacteria cells is 30 then:

• a = 30

Therefore, the equation that can be used to determine the number of cells after x hours is:

`y=30(1.5)^x`

where:

• y = total amount of bacteria cells
• x = number of hours