Question

The amount of bacteria in a Petri dish increases at a rate proportional to the amount present. At time t=0, the amount of bacteria in the dish is 10 grams. At time t=2, the amount of the bacteria in the dish is 30 grams. What is the amount of bacteria in the dish at time t=6?

A. 70 grams
B. 190 grams
C. 270 grams
D. 9270 grams

Answer 1

C. 270 grams

Explanation:

-This is an exponential growth function which can be expressed using the formula:

`P_t=P_oe^(rt)`

Where:

• 
  `P_t` is the size at time t.
• 
  `P_o` is the initial size
• 
  `r` is the growth rate
• 
  `t` is the time

Given the size at t=2 and at t=0, we substitute in the growth function to solve for r:

`30=10e^(2r)\\\\3=e^(2r)\\\\r=(In \ 3)/(2)\\\\=0.54931`

We use this calculated rate to determine the population at t=6

`P_t=P_oe^(rt)\\\\=10e^{6* (In \ 3)/(2)}\\\\=270\ grams`

Hence, the bacteria's size at t=6 is 270 grams