Question

A culture started with 3,000 bacteria. After 8 hours, it grew to 3,300 bacteria. Predict how many bacteria will be present after 12 hours. Round your answer to the nearest whole number.

Answer 1

Answer:

$3,462\ bacteria$

Step-by-step explanation:

In this problem we have a exponential function of the form

$y=a(b^x)$

where

x is the time in hours

y is the numbers of bacteria

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

we have that

$a=3,000\ bacteria$

For x=8, y=3,300

substitute in the exponential function

$3,300=3,000(b^8)$

solve for b

$1.1=(b^8)$

$b=\sqrt[8]{1.1}$

$b=1.0120$

Find the value of r

$r=b-1=1.0120-1=0.0120=1.20\%$

The equation is equal to

$y=3,000(1.012^x)$

For x=12 hours

substitute the value of x in the equation

$y=3,000(1.012^{12})$

$y=3,462\ bacteria$