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.

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.