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:

-The growth of bacteria follows an exponential distribution expressed as:

`P_t=P_oe^(rt)`

Where:

• t=time
• 
  `r`=rate of growth

• 
  `P_o` is the initial size and'
• 
  `P_t` is the size at time t

Given the size at time t and time zero, we substitute in the function to calculate the rate of growth r:

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

#we use the calculated rate of growth to determine time at t=6:

`P_t=10e^(6* 0.54931)\\\\\\=270.00625\approx 270\ grams`

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