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

Question

The number of bacteria in a culture is increasing according to the law of exponential growth. After 3 hours, there are 400 bacteria, and after 6 hours, there are 3200 bacteria. How many bacteria will there be after 7 hours?

Answer 1

The bacteria double every hour (400, 800. 1600, 3200).

Th.erefore after the next hour there shall be 6400

Answer 2

we use the exponential growth equation y = ar^x where a is initial value and r is common ratio

so 400=ar^3

3200= ar^6

divide equation 2 by equation 1 and solve for r 8= r^3 so r =2

substitute r into first equation 400=a(2)^3. 400= 8a a=50

at 7 hours then y= 50(2)^7= 6400