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 = What will be the population in 10 years? (Round your answer to the nearest person.) persons How fast is the population growing at t = 10? (Round your answer to the nearest person.) persons/year

Part 1)

Part 2)

Part 3)

Step-by-step explanation:

In this problem we have a exponential growth function of the form

where

p_0 is the initial population

t is the number of years

r is the rate of change

we have that

The initial population p_0 has doubled in 5 years

so

substitute in the equation above

solve for r

elevated both sides to 1/5

substitute

Find the value of p_0

Remember that

the population is 9,000 after 3 years

so

substitute

so    

What will be the population in 10 years?

For t=10 years

substitute

How fast is the population growing at t = 10?

we know that

For t=0 ----> P=5,937.8 people

For t=10 ---> P=23,752 people

so

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.