Posted by **Billy** on Monday, October 22, 2012 at 12:40pm.

The population (in thousands) of the Tzitzit bird is well described by a function of the form P(t) = ae^kt, where t is the time in years and a and k are constants. If the population was 10 thousand when t-0 and 300 thousand when t=3, determine the constants a and k exactly. Then use the formula for P(t) to find the population when t=(4)

- Calculus -
**Steve**, Monday, October 22, 2012 at 2:25pm
10000 = ae^0 --> a=10000

300000 = 10000 e^3k

30 = e^3k

3k = ln30

k = 1/3 ln30

P(t) = 10000 * e^(t/3 ln30)

P(4) = 10000 * e^(4/3 ln30) = 932170

Note that since e^ln30 = 30,

P(t) = 10000 * 30^(t/3)

but to evaluate that, you need to fall back to logs anyway.

What it means is that the population grows by a factor of 30 every 3 years. But then, we knew that from the initial conditions given: P(3) = 30*P()

## Answer This Question

## Related Questions

- math - Suppose that the population of a town is described by P=0.16t^2=7.2t=100...
- math - Suppose that the population of a town is described by P=0.16t^2+7.2t+100...
- Math - The population of a certain species of bird is limited by the type of ...
- College algebra - The population P of a city has been increasing at an annual ...
- Calculus - The rate of growth of a particular population is given by dP/dt=50t^2...
- math - The population of a small town is modelled by the function p(t)= 20(4t+3...
- MATH - 4. The population of a small town is modelled by the function p(t)= 20(4t...
- MATH - 4. The population of a small town is modelled by the function p(t)= 20(4t...
- Advance Functions - The population of a small town is modeled by the function p(...
- Calculus - The population of a colony of bacteria is modeled by the function p(...

More Related Questions