The count in a bateria culture was 100 after 20 minutes and 2000 after 30 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Find the doubling period. Find the population after 105 minutes. When will the population reach 11000. Answer: 0.25 Answer: 2.3137821315976 Answer: 11448668044799 Answer: 35.690588933089

Question

The count in a bateria culture was 100 after 20 minutes and 2000 after 30 minutes. Assuming the count grows exponentially,  What was the initial size of the culture?        Find the doubling period.        Find the population after 105 minutes.        When will the population reach 11000.      Answer: 0.25 Answer: 2.3137821315976 Answer: 11448668044799 Answer: 35.690588933089

campbell_st · Answer

well I'll assume that the exponential growth formula is 

$$A = A_{0}e^{kt}$$

so start by find k. the growth constant 

using t = 10, A0 = 100 a = 2000

$$2000 = 100 e^{10k}$$

then 

$$\ln(20) = 10k$$

solve for k. 

then use the 20 minute information and substitute your value of k

$$100 = A_{0} e^{20 \times k}$$

then 

$$A_{0} = \frac{100}{e^{20k}}$$

will give the initial population. 

the rest should be straight forward from here