Question

The population of a region is growing exponentially. There were 20 million people in 1990 (t = 0) and 66 million in 2000.

Find an expression for the population at any time t, in years. Use the general exponential function and remember to use exact values.
P(t) =


What population would you predict for the year 2010?

What is the doubling time? (Round your answer to one decimal place.)

Answer 1

Are you given the sample exponential function P(t)?

Answer 2

no

Answer 3

ok, exponential functions are of the form
\[P(t)=A \times {10}^{Bt}\]
we need to find A and B which are constants !
it's given that "There were 20 million people in 1990 (t = 0)"
put t= 0 and P(t)= 20 million to find A
Could you do that?

Answer 4

So t=0 and b=??

Answer 5

you need to find the value of A, once we get A then we'll find B

Answer 6

20,000,000=A*10^B0

Answer 7

yeah, so what would you get for A?

Answer 8

please help me this is due in 10 mins :(

Answer 9

@Brent0423
\[20000000=A 10^{B\times 0}\]
\[20000000=A \]

Answer 10

ok

Answer 11

8 mins :( im freaking out, can u please give me the answers then u can go back and explain

Answer 12

8 minutes are enough, we'll solve it:)
now you have A=20 million
Population grows to 66 million in 2000 so t=2000-1990=10 years
\[P(t)=A10^{BT}\]
\[66million=10 million *10^{B\times 10}\]
now find B, you'll need to use calculator

Answer 13

theres 3 parts to this problem

Answer 14

please just help me answer all 3 parts then we can go back, i will fail the assignment if i dont get this problem right

Answer 15

4 mins :(

Answer 16

you'll get
\[66/20= 10^{B*10}\]
\[B=\frac{\log 3.3}{10}\]
it's just matter of 2 minutes, tell me the value of B

Answer 17

.051

Answer 18

now we need to find for 2010
t=2010-1990=20
so
\[P(20)=20 million \times 10^{0.051\times 20}\]
find population in 2010 from this

Answer 19

B=0.081 I just checked

Answer 20

no you were right sorry
b=0.051
find the population

Answer 21

@Brent0423 ??