Calculus question...
1. Suppose we have a population that increases according to the formula P(t) = P_{0} e^{kt}. Our goal is to fill out the following table:
Point 
t 
P(t) 
A 
0 

B 
10 
20 
C 
30 
50 
D 
40 

E 
2000 
(i) Use points B and C to write two equations. Then use them to solve for P_{0} and k. Finally, write the population equation.
(ii) Use (i) to fill in the rest of the chart. You may round each value to the nearest tenth.
(iii) Now use your formula to determine the doubling time of this population.
(iv) Explain how, without using an equation, you can now calculate the t values for which P(t) equals 1000. And how about 250? Do this by writing a clear brief essay, with complete English sentences.
(v) Now on graph paper, draw a clear graph of this exponential function. Be sure to label your axes, and to label, with their coordinate, each of points A through E.
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