precalc
posted by maddy .
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?

precalc 
bobpursley
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).
Respond to this Question
Similar Questions

PreCalc (Followup 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 … 
Econ
A firm is considering locating a 100 employee microprocessor production facility in one of Alandâ€™s cities. The products this firm will produce are expected to be exported to other places (other cities within and outside the country). … 
statistics
Suppose you are trying to estimate the percent of women in a city. Other things being equal, a simple random sample of 0.1% of the population of a city that has 2,000,000 people is ________ as a simple random sample of 0.1% of the … 
statistics
Suppose you are trying to estimate the percent of women in a city. Other things being equal, a simple random sample of 0.1% of the population of a city that has 2,000,000 people is ________ as a simple random sample of 0.1% of the … 
exponential equations
The City of South Bay has a current population of 85 000. If the city is increasing at a rate of 7.25% per year, calculate the future population in 8 years time. Round to the nearest person. 
exponential equations
The City of South Bay has a current population of 85 000. If the city is increasing at a rate of 7.25% per year, calculate the future population in 8 years time. Round to the nearest person. 
Intermediate Algebra
The amount P of pollution varies directly with the population N of people. City A has a population of 468,000 and produces 260,000 tons of pollutants. Find how many tons of pollution we should expect City B to produce, if we know that … 
probability
An installation technician for a specialized communication system is dispatched to a city only when three or more orders have been placed. Suppose that orders follow a Poisson distribution with a mean of 0.25 per week for a city with … 
Math
The population in a 55 square mile city, City A, is 44,000. A neighboring city, City B, measures 65 square miles and has 48,750 citizens. Determine which city has a greater population density and by what percentage its population density … 
Pre calc
The population of a Midwestern city decays exponentially. If the population decreased from 900,000 to 800,000 from 2003 to 2005, what will be the population in 2008?