The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours, there are 50 bacteria, and after 5 hours, there are 400 bacteria. How many bacteria will there be after 7 hours?

Given:

The number of bacteria in a culture is increasing according to the law of exponential growth.

After 2 hours, there are 50 bacteria, and after 5 hours, there are 400 bacteria.

To find:

The number of bacteria after 7 hours.

Solution:

Let y be the number of bacteria after x hours.

The general exponential growth model is

where, a is initial value and b is growth factor.

After 2 hours, there are 50 bacteria. So, the point is (2,50). Put x=2 and y=50.

        ...(ii)

After 5 hours, there are 400 bacteria. So, the point is (5,400). Put x=5 and y=400 in general exponential growth model.

      ...(iii)

Divide equation (iii) by (ii).

Taking cube root on both sides, we get

Put b=2 in (ii).

Put a=12.5 and b=2 in (i).

This is the equation which represents number of bacteria after x hours.

Put x=7 in the above equation.

Therefore, the number of bacteria after 7 hours is 1600.

ik how do do this just give me a few minutes and i will give it to

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer