Aculture started with 5,000 bacteria. after 4 hours, it grew to 6,000 bacteria. predict how many bacteria will be present after 17 hours. round your answer to the nearest whole number.

y = 10852 bacteria

Step-by-step explanation:

The equation is exponential growth

y = a  b^x  where a is the initial amount , b is the growth rate and x is the time

At time 0, we have 5000 bacteria

5000 = a * b^0

5000 = a *1

a = 1

At 4 hours, we have 6000 bacteria

6000 = 5000 * b^4

Divide each side by 5000

6000/5000 = b^4

6/5 = b^4

Take the 4th root of each side

(6/5)^(1/4) = (b^4)^(1/4)

1.046635139 = b

Our equation is

y = 5000 (1.046635139) ^ x

We want to find the number of bacteria present after 17 hours

y = 5000 (1.046635139)^17

y=10851.51313

To the nearest whole number

y = 10852 bacteria

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