The amount of bacteria growing in a dish is given by the model N(t) = 450e0.175t, where t represents time in hours and N(t) represents number of bacteria.

Question

The amount of bacteria growing in a dish is given by the model N(t) = 450e^0.175t, where t represents time in hours and N(t) represents number of bacteria.

a) Find and interpret N(0).

b) What is the number of bacteria after 6 hours?

c) When will there be approximately 7129 bacteria present in the dish?

Answer 1

This is an easy question, Jennifer. I'll give you some tips and I'm sure you can do the rest.  It won't help you if I do it for you :)


a) N(0)=450e^(0.175*0). So, N(0)=450. The interpretation is that this is the number of bacteria you started with, before any time elapsed, before it got a chance to multiply
b) After 6 hours, t=6 and the number of bacteria is N(6). So plug 6 in your model to replace t and calculate N(6).
c) Now you have to find t when N(t)=7129. Set 450e^(0.175t)=7129 and solve for t.