SOLUTION: `Can someone please help me solve this problem: In 2000 the population of a town was 35000. In 2010 it was 50000. Find an exponential model of the form f(t)=A base 0 e^kt for this

Question 1082600: `Can someone please help me solve this problem: In 2000 the population of a town was 35000. In 2010 it was 50000. Find an exponential model of the form f(t)=A base 0 e^kt for this population, where t is time in years since 2000. I also need help finding K but I think you have to use Ln logarithm but I am not sure.
B) what year would the population reach 100,000?

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The exponential growth/decay model is
:
A = A(o) * e^kt, where A(o) is the amount we start with, k is the constant of growth or decay, t is time
:
A) 50000 = 35000 * e^10k
:
e^10k = 50000 / 35000 = 1.4286
:
10k = ln 1.4286 = 0.3567
:
*************************
k = 0.3567 / 10 = 0.03567
*************************
:
B) 100000 = 35000 * e^(0.03567t)
:
e^(0.03567t) = 100000 / 35000 = 2.8571
:
0.03567t = ln 2.8571 = 1.0498
:
t = 1.0498 / 0.03567 = 29.4309 approx 29
:
*******************************************
the population will be 100000 in year 2029
*******************************************
:

RELATED QUESTIONS
Can someone please help me solve this problem: In 2000 the population of a town was... (answered by josmiceli)

Can someone help me solve this problem? South America population in 1900 was... (answered by atif.muhammad)

the population of a town in 2010 was 1800000 and in 2011 it was 2100000. find the percent (answered by TimothyLamb)

I would appreciate if someone could take time out of their day and help me with my... (answered by ankor@dixie-net.com)

Could someone help me with this problem? Suppose a town experiences population decline... (answered by stanbon)

Please help me solve this word problem: A town census shows population of 2400 in 1980... (answered by stanbon)

can you please help me solve this problem?? In a particular small town, the... (answered by ankor@dixie-net.com,stanbon)

HELP this is my last question before I have to hand this in in an hour, can someone help... (answered by stanbon)

Two neighboring towns have had population changes over a ten year period that follow... (answered by stanbon)