Suppose y left parenthesis t right parenthesis equals 35 e to the power of 3 t end exponent plus 57 represents the number of bacteria present at time t minutes. at what time will the population reach 200 bacteria? (note: answers are expressed in terms of the natural logarithm)

For this case we have the following equation:

y (t) = 35 * exp (3t) + 57

For 200 bacteria we have:

200 = 35 * exp (3t) + 57

Clearing t we have:

exp (3t) = (200-57) / 35

exp (3t) = 4.085714286

ln (exp (3t)) = ln (4.085714286)

3t = ln (4.085714286)

t = ln (4.085714286) / 3

t = 0.5 minutes

Answer:

the population will reach 200 bacteria at:

t = 0.5 minutes

or

t = ln (4.09) / 3