The population P of a bacteria culture is modeled by P = 4100e^kt where t is the time inhours. If the population of the culture was 5800 after 40 hours, how long does it take forthe population to double? Round to the nearest tenth of an hour.Show work please A LOT OF POINTS

Accepted Solution

Enter the given values into the equation and solve.5800 = 4100e^(k*40)Divide both sides by 4100 and simplify:58 / 41 = e^(k*40)Remove e by taking the logarithm of both sides:ln(58/41) = k *40Divide both sides by 40:k = ln(58/41)/40k = 0.00867Now for the population to double set up the equation:2*4100 = 4100e^ktThe 4100 cancels out on both sides:2 = e^ktTake the logarithm of both sides:ln(2) = k*tDivide both sides by kt = ln(2) /kreplace k with the value from above:t = ln(2) / 0.00867t = 79.95 Rounded to the nearest tenth = 80.0 hours to double.