Question

A culture started with 3000 bacteria. After 4 hours, it grew to 3,600 bacteria. Predict how many bacteria will be present after 10 hours. Round your answer to the nearest whole number. Use exponential growth formula

Answer 1

Hello Shannonrodrigue. You can solve this by setting up an exponential growth equation.


`A = A_ob^t`

`3600 = 3000b^4`

Now we solve for b

`3600 = 3000b^4`

`(3600)/(3000) = (3000b^(4))/(3000)`

`(6)/(5) = b^4`

`\sqrt[4]{(6)/(5)} = \sqrt[4]{b^4}`

`\sqrt[4]{(6)/(5)} = b`

Now that we have found b, we can use the equation
`A = 3000b^t` to predict how many bacteria will be present after 10 hours.

`b = \sqrt[4]{(6)/(5)}`
t = 10

`A = 3000b^t`

`A = 3000\sqrt[4]{(6)/(5)}^(10) = 4732.3228 = 4732`

Answer = 4732