Question

Note: when solving for K, round to the four decimal place.
A country's population in 1995 was 184 million. in 2002 it was 188 million. estimate the population in 2006 using exponential growth formula. round your answer to the nearest millions?

Answer 1

we can do this quickly

Answer 2

increased by a factor of \(\frac{188}{184}=\frac{47}{46}\)in 7years, you can use the formula
\[184\times\left( \frac{47}{46}\right)^{\frac{t}{7}}\]

Answer 3

i dont under stand this at all and i am really good at math

Answer 4

want to go slow?

Answer 5

yes that wuld be very helpful

Answer 6

the method i wrote above is a quick and easy method to solve this, but is not what your math teacher does, and does not involve \(k\)
you want to do it the math teacher way? find the \(k\) etc?

Answer 7

i dont have a teacher i have a computer lol

Answer 8

oh so you only need to put in an answer, right? if so we can do it the quick way!

Answer 9

yeah

Answer 10

A country's population in 1995 was 184 million. in 2002 it was 188 million. estimate the population in 2006 using exponential growth formula. round your answer to the nearest millions?

we will use only the numbers given
184
188
7

Answer 11

ok

Answer 12

ok you don't see a 7, but from 1995 to 2002 is 7 years

Answer 13

ok then what

Answer 14

in other words, the first thing we do (mentally) is start counting by making 1995 year 0, that makes 2002 year 7 and 2006 year 11

Answer 15

the population increases from 184 to 188 for a factor of
\[\frac{188}{184}=\frac{47}{46}\]
this will be the base of the exponential

Answer 16

the initial population when you start counting is \(184\) and the time it takes to increase by this factor is \(7\) we go right to
\[\large P=184\times \left(\frac{47}{46}\right)^{\frac{t}{7}}\]

Answer 17

you want year 11, (2006) so replace \(t\) by \(11\) and use a calcualtor to compute
\[\large P=184\times \left(\frac{47}{46}\right)^{\frac{11}{7}}\]

Answer 18

careful with the calculator, it is easy to make a mistake

Answer 19

since you are already on a computer i would use this
http://www.wolframalpha.com/input/?i=184%2847%2F46%29^%2811%2F7%29

Answer 20

again, this is not the way it is done in your on line course, or whatever, but it is easy because all we used were the numbers given to you
\[184,188,7\]

Answer 21

ok thanks that helped me

Answer 22

@satellite73

Answer 23

yw
hope you see the method