The population P of a fish farm in t years is modeled by the equation

Question

P(t)=1500/1+9e-0.6t
To the nearest tenth, how long will it take for the population to reach 900?

Answer 1

To find out how long it will take for the population to reach 900, we need to solve the equation:

900 = 1500 / (1 + 9e^(-0.6t))

First, we can multiply both sides by the denominator to get rid of it:

900(1 + 9e^(-0.6t)) = 1500

Next, we can divide both sides by 1500:

0.6e^(-0.6t) + 1 = 0.6

Subtracting 1 from both sides gives:

0.6e^(-0.6t) = -0.4

Finally, we can divide both sides by 0.6:

e^(-0.6t) = -0.4/0.6 = -0.6667

This is not possible, since e^(-0.6t) is always positive. Therefore, there is no solution to this equation, and the population will never reach 900.