The population of a town is 81,712 and declines continuously at a rate of 4.1% each year. What is the approximate population of the town in 17 years?

Question

anonymous · Answer

Will give medal!!!!!!

anonymous · Answer

This will use the formula for exponential decay

anonymous · Answer

$$P=P _{0}e ^{rt}$$

anonymous · Answer

can you please help explain in words?

anonymous · Answer

what do i plug it into??

anonymous · Answer

$$P=81712e ^{-(.041*17)}$$

anonymous · Answer

I just plugged in all the values for you into the equation I pasted earlier

anonymous · Answer

whats the e for ?

anonymous · Answer

all you have to do is solve on the caluclator and the value of P will give you the approximate population in 17 years

anonymous · Answer

e is euler's constant or the exponential growth constant

anonymous · Answer

e~2.71828 if you don't have it on your calculator

anonymous · Answer

so do i raise e by .041*17?

anonymous · Answer

yes and multiply it by the negative for decay

anonymous · Answer

i got -154,815..... thats not right....

anonymous · Answer

no check your math again

anonymous · Answer

JK!!!!! i got 40,698

anonymous · Answer

try multiplying .041 and 17 and -1 first then raise it over e

anonymous · Answer

well done thats it

anonymous · Answer

so what about The population of a city is 83,945 and grows continuously at a rate of 1.3% each year. What is the approximate population of the city in 21 years?

anonymous · Answer

so for this one you want to solve the same way except use a positive value for the exponential power

anonymous · Answer

$$P=83945e ^{.013*21}$$