Exponential Growth Problem

Question

The count in a bacteria culture was 700 after 15 minutes and 1700 after 40 minutes.

What was the initial size of the culture? (______) 

Round your answer to the nearest bacteria.

Find the doubling period.(_______)  Round your answer to one decimal place.

Find the population after 120 minutes. (______) Round your answer to the nearest bacteria.

When will the population reach 14000? (________) Round your answer to one decimal place.

Answer 1

initial is about 410

doubling period 19 minutes

about 29,677 after 120 minutes

about 99 minutes for 14,000

count = 410(8.50558)^t where t=time in hours

8.50558 is e^2.13 where 2.13=r

in 15 minutes it doesn't quite double, as it only took 15 minutes

120 minutes is over 6 doubling periods

99 minutes is over 5 doubling periods

410 initially

820 after 1

1640 after 2

3280 after 3

6560 after 4

13120 after 5

26240 after 6