Question

A city had population 67,255 on january 1, 2000, and its population has been increasing by 2935 people each year since then. A linear model for the population p, where t is in years after 2000, is

a.P(t) = 2935t.
b.P(t) = 67255t.
c.P(t) = 2935 + 67255t.
d.P(t) = 67255 + 2935t.

Answer 1

P(t) = 67255 + 2935t is correct. The figure 67255 does not change, while 2935 is added each time t increases.

Answer 2

We are given: On january 1, 2000 initial population = 67,255.

Number of people increase each year = 2935 people.

Therefore, 67,255 would be fix value and 2935 is the rate at which population increase.

Let us assume there would be t number of years after year 2000 and population P after t years is taken by function P(t).

So, we can setup an equation as

Total population after t years = Number of t years * rate of increase of population + fix given population.

In terms of function it can be written as

P(t) = t * 2935 + 67255.

Therefore, final function would be

P(t) = 2935t +67255.

So, the correct option is d.P(t) = 67255 + 2935t.