Calculus

posted by Brian

assuming the population of the earth changes at a rate proportional to the current population further, it is estimated that at time t=0, the earth's population was 600 million, at t=300, it's population was 2.8 billion. find an expression giving the population of the earth at anytime. assuming that the greatest population the earth can support is 25 billion, when will this limit be reached?

1. Scott

continuous growth ... p e^(rt)

2.8E9 = 6E8 e^(300r)

ln(28/6) = 300 r ... solve for r

2.5E10 = 6E8 e^(rt) ... solve for t

Similar Questions

1. calculus

Bacterial Population: A bacterial colony is estimated to have a population of P(t)=(24t+10)/(t^2+1) Million t hours after the introduction or a toxin. At what rate is the population changing in 1 hour after the toxin is introduced …
2. College Algebra

The population of the Earth is approximately 6 billion people and is growing at an annual rate of 1.9%. Assuming a Malthusian growth model, find the world population in 44 years.
3. Calculus AB

The rate of growth dP/dt of a population of bacteria is proportional to the square root of t, where p is the population size and t is the time in days (0<equal t <equal 10). That is, dp/dt = ksqrt(t). The initial size of the …
4. calculus

The population of a certain community is increasing at a rate directly proportional to the population at any time t. In the last yr, the population has doubled. How long will it take for the population to triple?
5. maths --plse help me..

A bacteria culture has an initial population of 600. After 4 hours the population has grown to 1200. Assuming the culture grows at a rate proportional to the size of the population, find the function representing the population size …
6. Calculus

The population in certain country is growing at the rate of 7 % a year . If the population in the year 1995 was 190 million, (a)determine an exponential expression representing the population as a function of the year. (b) What will …
7. Math

The population of the Earth is approximately 6 billion people and is growing at an annual rate of 1.9%. Assuming a Malthusian growth model, find the world population in 42 years
8. calculus

The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.3. The initial population is 40. (1) What is the population after 30 …
9. 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 …
10. Calculus

Assuming the population of the earth changes at a rate proportional to the current population further, it is estimated that at time t=0, the earth's population was 600 million, at t=300, it's population was 2.8 billion. find an expression …

More Similar Questions