Question

A population of bacteria is growing according to the equation P ( t ) = 1100 e 0.07 t . Estimate when the population will exceed 1594.

t=

Answer 1

A population of bacteria is growing according to the equation P(t) = 1100e^0.07t where P(t) is the population of bacteria after t units of time. When P(t) > 1594, we have 1100e ^0.07t> 1594 or, e^0.07t > (1594/1100). Now, on taking natural logarithm of both the sides, we get ln(e ^0.07t) > ln (1594/1100) or, 0.07t ln e > 0.3709364 or, 0.07t > 0.3709364 so that t >0.3709364 /0.07 or, t > 5.299091429 or, t > 5.3 units of time ( on rounding off to 1 decimal place). Thus, the bacteria population will exceed 1594 after 5.3 units of time.    

t = 5.3