Question

1. A colony of bacteria grows exponentially according to the function where N is measured in grams and t is measured in days.

N(t)=100e^0.045t

You may use graphical method or algebraic method. Please show work if algebraic or show the graph if graphical method - round to 2 decimals.

a. Determine the initial amount of bacteria: ____________________________

b. What is the population after 5 days: _______________________________

c. How long will it take the population to reach 140 grams:_______________

Answer 1

N(t) = 100*e^0.045t.

a. N(0) = 100*e^0 = 100*1 = 100 g.

b. N(5) = 100*e^(0.045*5) = 100*e^0.225 = 125.2 g.

c. N = 100*e^0.045t = 140 g.
100*e^0.045t = 140.
e^0.045t = 140/100 = 1.40.
Take Ln of both sides:
0.045t*Lne = Ln1.40.
0.045t = Ln1.40 / Lne = 0.33647.
t = 0.33647 / 0.045 = 7.5 Days.