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 formulaP = 185(2)(0.05t)where t is measured in years. The town was populated in 1880. What was the population (to the nearest 1,000) in the year 2000?

Answer 1

Is formula
185*2*0.05t

Answer 2

?

Answer 3

no im sorry the formula is 185(2)^(0.05t)

Answer 4

I think you mean:
P(t) = \[185(2)^{(0.05t)}\]
so if you subtract 2000-1880 to get t then substitute that into the equation.

Answer 5

t should be 120
120*.05 = 6
2^6 = 64
185*64 = 11840 people

Answer 6

or 12,000 people if you round

Answer 7

okay just to double check your answer, heres additional informatio. the population of the year 1880 was 185,000

Answer 8

then in that case set 1880= 185(2)^(0.05t) and solve for t. Add 120 to the t value and substitute that value back into the P(t)

Answer 9

and what did u come up with because im stuck

Answer 10

from 1880 to 2000, 120 years have passed so this will be the t_value you use to evaluate the population in year 2000
\[P = 185*2^{.05*120}\]
\[P = 185*2^{6}\]
\[P = 11,840\]
since this is in thousands add 3 zeroes

Answer 11

wouldnt you add 11,840 to the population 185,000 because thats how much the popultion increased over 120 years?

Answer 12

no because we left the 185 in the equation their initial population is already factored in
the increase would be 11,840 - 185

Answer 13

in other words the equation gives population at any time t not just the increase

Answer 14

damn. well then maybe idid it wrong and maybe the population of 1880 isnt 185,000 .....ughh im confusing myself.

Answer 15

??????????????????

Answer 16

If what you posted above is correct then yes when t=0 in 1880 the population is 185,000