Question

Twenty years ago a small town in Texas had a population of 10,000. The population has increased 8% each year since then. What is the current population of this town?

Answer 1

well,so if we imagine the population of that village was x twenty years ago...we can find it's population for next year: \(\large (\frac{ 8 }{ 100 } \times x ) + x\)

Answer 2

ok so the next year would be 10800

Answer 3

\( \large \frac{ 8 }{ 100 } ((\frac{ 8 }{ 100 } \times x) + x) + (\frac{ 8 }{ 100 } + x ) = (\frac{ 8^2 }{ 100^2 } \times x) + \frac{ 8 }{ 100 } \times x + (\frac{ 8 }{ 100 } + x ) \)

Answer 4

and it's for next 2 years ... we can simply use it for next twenty years.

Answer 5

so i plugin 10000 for x?

Answer 6

so about 46609

Answer 7

no , I want to make a formula that would gives us the values for each years! i'm trying to do this...if you want to find the population of that village for every year it would take a long time and you have to do it for 20 times! so it would be easier i we only find a formula.

Answer 8

The equation of an exponential equation is in the form y =a(b)^x

The variable "a" is always the initial value. Which in this case is 10,000. To think about why this makes sense, imagine if x was set = 0. Well that would make b = 1 and 1*10,000 = 10,000. Meaning that a is always the initial value/y-intercept.

b = to the growth rate. Since it is 8%, that means b = 1.08

So you get an equation of y=10000(1.08)^x plug x=2 and see what you get.