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olga nikolaevna [1]
3 years ago
5

A culture started with 3000 bacteria. After 2 hours it grew to 3300 bacteria. Predict how many bacteria will be present after 16

hours. Round your answer to the nearest whole number.
Mathematics
1 answer:
bixtya [17]3 years ago
6 0

Answer:

6,430\ bacteria

Step-by-step explanation:

we have a exponential function of the form

y=a(1+r)^{x}

where

y is the population of bacteria

a is the initial value

r is the rate of growth

x is the number of hours

we have

a=3,000 bacteria

y=3,000(1+r)^{x}

For x=2, y=3,300

substitute

3,300=3,000(1+r)^{2}

(3,300/3,000)=(1+r)^{2}

Apply square root both sides

1+r=\sqrt{3.3/3}

r=\sqrt{3.3/3}-1

r=0.0488

r=4.88\%

substitute in the equation

y=3,000(1+0.0488)^{x}

y=3,000(1.0488)^{x}

<u><em>Predict how many bacteria will be present after 16 hours</em></u>

For x=16 hours

substitute

y=3,000(1.0488)^{16}

y=6,430\ bacteria

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