1. ## stupid test question.

i DO understand how to do this, i just cant remember how to get all of the numbers in the equation in order to solve it.
"The population of a town is 10000 people. it grows at a rate of 1.4% per year for four years, what is the growth factor, b, for the equation y=a*bx (x being the small integer over the b)"

i get that a = 10000
i get that b = 1.4
i get that x = 4
but none of the answers i come out with is in the multiple choice.

2. Originally Posted by autumn
i DO understand how to do this, i just cant remember how to get all of the numbers in the equation in order to solve it.
"The population of a town is 10000 people. it grows at a rate of 1.4% per year for four years, what is the growth factor, b, for the equation y=a*bx (x being the small integer over the b)"

i get that a = 10000
i get that b = 1.4 <<<<<<<< where did you get this number from?
i get that x = 4
but none of the answers i come out with is in the multiple choice.
1. If x = 1 then the population is:

$p = 10000 + \frac{1.4}{100} \cdot 10000 = 10140$

2. Plug in these values and calculate the value of b.

3. Hello, autumn!

Your explanation could be clearer . . .

The population of a town is 10,000 people.
It grows at a rate of 1.4% per year for four years.
Find the growth factor $b$ for the equation: . $y\:=\:a\cdot b^x$

When $x = 0,\;y = 10,\!000$

We have: . $10,\!000 \:=\:a\cdot b^0 \quad\Rightarrow\quad a \,=\,10,\!000$

. . The function is: . $y \:=\:10,\!000\cdot b^x$

A little baby-talk:

After one year $(t = 1)$, the population increased by 1.4%.
. . The increase is: . $0.014 \times 10,\!000 \,=\,140$
Hence, the new population is: $10,\!140$

We have: . $10,\!140 \:=\:10,\!000\cdot b^1 \quad\Rightarrow\quad b \:=\:\frac{10,\!140}{10,\!000}$

Therefore, the growth factor is: . $\boxed{b \:=\:1.014}$

. . The population function is: . $y \;=\;10,\!000\cdot 1.014^x$

4. ## hmmm. thanks.

thank you. these answers will realy help me in the long run if i just sit and mess with that formula.
i feel stupid asking such a simple question though.

5. ## explination

i got the 1.4 because it is the population growth rate. population times growth rate to the power of the number of years. am i wrong?

6. Originally Posted by autumn
i DO understand how to do this, i just cant remember how to get all of the numbers in the equation in order to solve it.
"The population of a town is 10000 people. it grows at a rate of 1.4% per year for four years, what is the growth factor, b, for the equation y=a*bx (x being the small integer over the b)"

i get that a = 10000
i get that b = 1.4
i get that x = 4
but none of the answers i come out with is in the multiple choice.

Hi Autuum,

So what did you get for the growth factor.Did you divide the % increase by 100? How many people will there be after one year? Can you see how to expand for 4 years?

bjh

7. Originally Posted by autumn
i got the 1.4 because it is the population growth rate. population times growth rate to the power of the number of years. am i wrong?
You got 1.4 for what? The rate of change was given as 1.4% or 0.014 so the population will increase by 0.14 of the original amount. Added to the original amount, the population will be 1.014 of the original amount which means that in one year the population is multiplied by 1.014. That, as Soroban told you, is b.

8. ## i get it now

at first i couldnt remember to divide the percentage (or 0.14) by the original number. i knew i was missing a step, but i couldnt find it. but now it makes a lot of sence. im dont have an algabra teacher. im on my own in this subject, hence my ignorence. your help is appreceated.
(also... please disregard my spelling. or lack there of)