The present population, P, in thousands, of a town is related to the initial population of the town at.......?

Question

The present population, P, in thousands, of a town is related to the initial population of the town at time t = 0 by the formula

P = 125(3)^(0.05t)

where t is measured in years. The town was populated in 1880.
What was the population of the town in 1880?

DON'T forget about the "in thousands" part.

What was the population (to the nearest 1,000) in the year 2000?

Answer 1

Since 1880 is "t=0" ("the town was populated in 1880")...

P = 125(3)^(0.05t)
P = 125 * 3^(0.05*0)
P = 125 * 3^0
P = 125 * 1
P = 125

Since P is in thousands, the population is 125,000 as of 1880.

Now, for 2000... since we are using 1880 for "year 0", 2000 would be t = (2000-1880) = 120.

P = 125(3)^(0.05t)
P = 125 * 3^(0.05 * 120)
P = 125 * 3^6
P = 125 * 729
P = 91,125

Since P is in thousands, the population in 2000 would be 91,125,000. That seems a bit excessive. Is it possible that there is a typo in your equation (maybe .005t instead of 0.05t, or maybe 0.125 instead of 125?)

Answer 2

You need more information

Either a year that the town was established....or an example of the population in a particular year.

In year 0, the population was 125 thousand. There is no way to tell how close this is to 1880 or 2000 without more information.

Answer 3

That's a straightforward application of the formula.

P(t) = 125*3^(0.05t)

in 1880, t = 0
P(0) = 125 k

In 2000, t = 120
P(120) = 125 * 729 = 91125 k

Answer 4

1888=8000

Not sure, actually