Question

The number of people living in a country is increasing each year exponentially so that the number of people 5 years ago was 4 million.
The number of people in five years time is projected to be 6.25 million.

What is the present population of the country?

Answer 1

I have no idea what this is. Help plz!

Answer 2

@AZ

Answer 3

@Angle

Answer 4

Can someone help me plz?

Answer 5

@Angle @AZ can someone help me plz

Answer 6

uh I can try, but I gotta go teach it to myself first lol

here is what I'm thinking so far...
We have two points:
(-5, 4)
and
(5, 6.25)

we are looking for
1. the equation
2. the value of y for (0, y)

Answer 7

lol

Answer 8

ok so how do i do that

Answer 9

I googled "how to find exponential equation given two points" and now I'm reading this
https://sciencing.com/exponential-equation-two-points-8117999.html

Answer 10

Can't you just use the five years ago as a starting point for the exponential equation

So you initially start off with 4 million and in 10 years you'll have 6.25 million

and then once you get the rate, you can just find the population in 5 years which would be the current time

Answer 11

umm idek my teacher didn't explain it very good

Answer 12

would it be 5.125 million?

Answer 13

oh so like...
(0, 4)
and
(10, 6.25)

and we looking for (5, y)

Answer 14

Yeah, it would make it much easier to solve

Answer 15

\(\color{#0cbb34}{\text{Originally Posted by}}\) @aevans182
would it be 5.125 million?
\(\color{#0cbb34}{\text{End of Quote}}\)

close but not quite I think

Answer 16

oh umm 5 million?

Answer 17

\(y = ab^x\)

this is the format we plan on using to try to create an equation

we are going to temporarily plug in (0, 4) in order to solve for a or b

Answer 18

\(4 = a~b~^0\)

Answer 19

what is \(b^0\) = ?

Answer 20

1?

Answer 21

im so confused

Answer 22

great!

so then what is "a" equal to?

Answer 23

\(4 = a \times 1\)

Answer 24

4

Answer 25

ok so our formula is \(y = 4~b~^x\) so far

we are going to temporarily plug in the point (10, 6.25) and try to solve for b

Answer 26

I will give an example when Angle in done.

Answer 27

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Katrin369
I will give an example when Angle in done.
\(\color{#0cbb34}{\text{End of Quote}}\)
An example I use.

Answer 28

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Katrin369
\(\color{#0cbb34}{\text{Originally Posted by}}\) @Katrin369
I will give an example when Angle in done.
\(\color{#0cbb34}{\text{End of Quote}}\)
An example I use.
\(\color{#0cbb34}{\text{End of Quote}}\)
That might help you.

Answer 29

\(6.25 = 4 \times b~^{10}\)

what would "b" be equal to?
(I would suggest using a calculator)

Answer 30

i got like a 9.3 number

Answer 31

9.31322575e-10 bytes^10

Answer 32

https://www.wolframalpha.com/input/?i=6.25%3D4b%5E10

Answer 33

what's it say the solutions are?

Answer 34

1.04564 and -1.04564

Answer 35

cool, let's just take the positive one
that's what b is equal to

Answer 36

now our equation is
\(y = 4(1.04564)^x\)

Answer 37

plug in x = 5

solve for y
that would be your answer

Answer 38

so 5

Answer 39

million
yes :)

Answer 40

oh ok thank you so much