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 solve for t, we can substitute P(t) = 900 into the equation and solve for t:

900 = 1500 / (1 + 9e^(-0.6t))
1 + 9e^(-0.6t) = 1500 / 900
1 + 9e^(-0.6t) = 1.6667
9e^(-0.6t) = 0.6667
e^(-0.6t) = 0.0741
-0.6t = ln(0.0741)
t = ln(0.0741) / (-0.6)
t ≈ 6.9 years

Therefore, it will take approximately 6.9 years for the population to reach 900.

Answer 2

impatient much?
Once is enough, thank you.
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