The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 9,000 after 3 years. What was the initial population P0? (Round your answer to one decimal place.) P0 = 5937.8 What will be the population in 10 years? (Round your answer to the nearest person.) 23751 persons How fast is the population growing at t = 10? (Round your answer to the nearest person.) 3293 persons/year

P0 = 5937.8 people

P(t = 10) = 23751 people

P'(t = 10) = 3293 persons/year

Step-by-step explanation:

Let the population has the formula of

Where P0 is the initial population at t = 0 and k is the constant that we are looking fore.

Since the population doubled after t = 5 years

So after t = 3 years, population is P = 9000:

After 10 years, population would be quadtripled (10 years is 2 times of 5 years):

The rate of change in population is the derivative of the population function with respect to t

So after t = 10 years the rate of change in population would be

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560