Suppose that the number of cell phones in the world increases by a total of 160% over a five-year period. What is the continuous growth rate for the number of cell phones in the world?
Continuous growth is exponential where you are looking at A*e(bx) for constant A and b. You need two values to solve for two independent equations but you know f(x+5) = 1.6*f(x) for some particular value of x and you can cancel A from both sides.
Can you use this to solve for b?
No, f(x) is a function: f(x) = Ae^(bx) where f(x+5) = Ae^(b[x+5]).
You are not multiplying a constant f by x: f is a function that takes a value for x and spits out a value called f(x).
1.6*f(x+5) = 1.6*A*e(b[x+5]) = 1.6Ae^[bx + 5b] = 1.6Ae^[bx]*e^[5b] = f(x).
Well, I just figured it out this way which was similar to my student's solution manual.. If the initial amount was 0, then... if it raised up to 160%, that means that it went up 2.6 times the original number. Then I can have this formula 2.6P=Pe^5r which is ln2.6/5