Question

In 1977 the population of the United States was about 220 million and in 1987 the population was about 242. Assuming that the growth of population of the United States is an exponential function determine the year in which the population will reach 500 million.

I need to find an equation for this but I haven't been able to figure it out

Answer 1

oh, remidia lol

all of these problems are based on the fact\[N = N_0 (R)^{t/h}\]

Answer 2

I know, but I dont know how to place things properly. I solved for 500 = 100(1.1)^ t/10 and got the wrong answer. Something in my equation is wrong (I think)

Answer 3

(220)*R^10=242

Answer 4

where N is the current amount

N-0 is the initial amount

R is the growth/decay rate (if R>1 growth, R<1 decay)

t is time

h is the rate life ( for example, it a bacteria increases it's population in 7 days where t is in weeks, h would be 7)

Answer 5

the given facts are telling you that initially there are 220
and after "10 years" there are 242

the idea here is that in 10years, the population grows by 42million when initially there were 220 million
since the population matters when you want to know how
fast it grows,

all we need now is the rate.
h is a variable that converts the time unit, so since we will
just be using "years" only, h =1 is fine.

so the eqn we can make is

\[242 = 200(R)^{10}\]

Answer 6

so R is apprx

\[1.21^{1/10}\]

Answer 7

if you want to consider

"population grows by 10th-rt(121)% per year"

but a more natural way to think is

"population grows by 121% per 10 years"

Answer 8

so you use the function\[N = N_0(R)^{t/10}\]

Answer 9

that way, you will figure out that R is just 1.21 and

\[500 = 200(1.21)^{t/10}\]

Answer 10

so you can solve for t

Answer 11

I got about 48 years later, so about 2025 ?

Answer 12

Thats what I got, but the choices are

A) 2054 B) 2057 C) 2060 D) 2063 E) 2066

I think the 200 might be wrong

Answer 13

ah, it was 220, wasn't it.
let me calculate it again

Answer 14

I got 2063 since it takes 86 years to grow that much

Answer 15

How did you find the 86? Ahhhh im so confused.