Question

A population of bacteria is growing according to the equation P ( t ) = 1050e^0.16t .

Use a graphing calculator to estimate when the population will exceed 2337.

t = Give your answer accurate to one decimal place

Answer 1

Answer:

t must be greater than 5.0

Step-by-step explanation:

P ( t ) = 1050e^0.16t

We want P(t) > 2337

2337 <  1050e^0.16t

Divide each side by 1050

2337/1050<  1050/1050 e^0.16t

Take the natural log of each side

ln (2337/1050)) < ln(e^0.16t )

ln (2337/1050) < 0.16t

Divide by .16

ln (2337/1050)/.16 < 0.16/.16t

ln (2337/1050)/.16 < t

5.00049<t