Question

A bacteria culture starting with 240 bacteria doubles every hour.Use your calculator to figure how many bacteria there will be after x number of hours. Graph the bacterial growth. Create a function to represent the growth of the bacteria. f(t)=abᵗ

a=
b=
How many bacteria will there be after 10 hours?

Answer 1

Based on an exponential growth function, the number of bacteria after 10 hours will be 24,576.

To find the number of bacteria after x hours, we can use the formula:

y = a (2ˣ)

Where:

The initial number of bacteria (240 in this case) = a

The number of hours after starting the bacteria culture = x

To graph the bacterial growth, we can plot the number of bacteria on the y-axis and the number of hours on the x-axis. Here's what the graph looks like:

y

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This graph is an exponential growth curve because the number of bacteria doubles every hour.

We can create an exponential growth function to represent the growth of the bacteria as follows:

y =
`ab^t`

The initial amount (240) = a

The growth factor (2) = b

The time in hours after starting the culture = t

Thus, the exponential function to represent the growth of the bacteria is:

f(t) = 240 *
`2^t`

To find the number of bacteria after 10 hours, we can plug in t = 10 into the function:

f(10) = 240 x 2¹⁰ = 24,576

Thus, there will be 24,576 bacteria after 10 hours.