Question

uppose y left parenthesis t right parenthesis equals 30 e to the power of 4 t end exponent plus 17 represents the number of bacteria present at time t minutes. At what time will the population reach 125 bacteria? (Note: Answers are expressed in terms of the natural logarithm)

Answer 1

`y(t) = 30e^(4t) + 17`

You want

`y(t) = 125`

Then,

`30e^(4t) + 17 = 125`

`30e^(4t) = 108\\\\e^(4t) = (54)/(15)\\4t = ln\left((54)/(15)\right)`

Therefore

`t =  (1)/(4)ln((54)/(15))` minutes