Question

Round final answers to 3 decimal places.

Answer 1

There are 651.335 million cells in the petri dish after 11 hours and the cells will reach 1 billion cells after 14.068 hours

How to determine the number of cells after 11 hours?

The given parameters are:

At t = 0, Bacteria = 140 million

At t = 6, Bacteria = 320 million

This can be represented as:

f(0) = 140

f(6) = 320

An exponential function is represented as:

f(t) = f(0) * r^t

When t = 6, we have:

320 = 140 * r^6

Divide both sides by 140

r^6 = 2.28571428571

Take the 6th root of both sides

r = 1.15

So, we have:

f(t) = f(0) * 1.15^t

Substitute f(0) = 140

f(t) = 140 * 1.15^t

After 11 hours, we have:

f(11) = 140 * 1.15^11

Evaluate

f(11) = 651.33

Hence, there are 651.335 million cells in the petri dish after 11 hours

Time to reach 1 billion cells

This means that

f(t) = 1 billion i.e. 1000 million

So, we have:

1000 = 140 * 1.15^t

Divide by 140

1.15^t = 7.14285714286

Take the logarithm of both sides

t * log(1.15) = log(7.14285714286)

Divide both sides by log(1.15)

t = 14.068

Hence, the cells will reach 1 billion cells after 14.068 hours

Read more about exponential functions at:

brainly.com/question/2456547

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