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. Required:
a, What was the initial population P0?
b. How fast is the population growing at t = 10?

Step-by-step explanation:

Let the initial population of a community be P0 and the population after time t is P(t).

If the population of a community is known to increase at a rate proportional to the number of people present at time t, this is expressed as:

at t = 5 years, P(t) = 2P0

substitute:

If the population is 9,000 after 3 years

at t = 3, P(t) = 9000

a) Substitute into the formula to get P0

Hence the initial population is approximately 5938.

b) In order to know how fast the population growing at t = 10, we will substitute t = 10 into the formula as shown:

Hence the population of the community after 10 years is approximately 23,746

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.