Pre-Calc (Follow-up with Bob Pursley)

For the below problem, I solved it as you suggested and got

k=.0486

When I did 300,000 = 122,000e^.0486t
I got about 18.5 years for when the sewer system would need to be updated.

Next, for how many people will the new system have to accommodate for the system to last 15 years before needing to be updated again,
Should I use 300,000 for the p(o)?

pre-calc - bobpursley, Friday, January 8, 2010 at 9:08pm
Population is usually exponential growth

P(t)=P(o)e^kt

P(o)=122000
find k from
180000=122000 e^kt
log of both sides
ln(180000)=ln(122000)+ kt
then t=8, solve for k

see if you can do it from there. find t when P(t)=300,000
then find p(15+the t you just found).

The city planners of bakersfield, CA are studying the current and future needs of the city. The sewage system they have in place now can support 300,000 residents. The current population of the city is 180,000, up from 122,000 eight years ago. Assuming that the population will continue to row at this rate, when will the sewer system need to be updated? How many people will the new have to accomodate for the system to last 15 years before needing to be updated again?

Ok, so I know that 180,000 - 122,000 is 58,000 so 58,000/122,000 = 47.5%
increas in eight years. I'm not sure where to go from here.

Should I be using the formula for exponential growth?

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1. yes, use 300,000 as P(o) and t as 15

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