Math Calculus Help
posted by Anonymous .
A population grows exponentially. If the population is 0.5sqrt(e) at one year and 0.5e at two years, what is it at 4 years?

we know that
p = ae^kt
using the known values,
√e/2 = ae^k
e/2 = ae^2k
divide to get
(e/2) / (√e/2) = e^k
√e = e^k
so, k = 1/2
now, we see that
√e/2 = ae^(1/2)
so a = 1/2
p(t) = 1/2 e^(t/2)
p(4) = 1/2 e^2
Respond to this Question
Similar Questions

precalculus
the population of a country is 65 millions if it grows exponentially in a rate of 1.5% annual 1.calculate the estimate population in 12 years 2.when the population increases 4 times could somebody please explain me this kind of problems … 
Calculus
The population of a region is growing exponentially. There were 40 million people in 1980 (when t=0) and 50 million people in 1990. Find an exponential model for the population (in millions of people) at any time t, in years after … 
Math
A city has a population of 30,000 people. Suppose that each year the population grows by 3.7% . What will the population be after 6 years? 
calculus
The population of a country was 8.4 million people in 2000. Three years later, the population of the same nation was 9.3 million people. Assuming that population is growing exponentially, what is the projected population (rounded to … 
college algebra
Suppose that the Russian population is declining by 0.48% each year, and continues to decline at this rate every year. a.) what is the overall 'growth' factor (really a decline factor) for 40 years of population decline? 
Calculus
The rate of growth of a particular population is given by dP/dt=50t^2100t^3/2 where P is the population size and t is the time in years. The initial population is 25,000. Find the population function. Estimate how many years it will … 
math
the population of the world in the year 1650 was about 500 millions ,and in the year 2010 was about 6756 million .assuming that the population of the world grows exponentially ,find the equation for the population P(t) in millions … 
Pre Calculus
17. population growing at an annual rate r will triple in a time t given by the formula t = ln 3/r If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple? 
Math
A population grows exponentially at a rate of 2.6% per year. How long will it take for the population to triple? 
Calculus
Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.21 percent a year and that the 1988 population was 6.8 million, write an expression for the population as a function of time in years. (Let t=0t=0 …