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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 :

opudodennis

Answer:

C. 270 grams

Step-by-step explanation:

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

[tex]P_t=P_oe^{rt}[/tex]

Where:

  • [tex]P_t[/tex]  is the size at time t.
  • [tex]P_o[/tex] is the initial size
  • [tex]r[/tex] is the growth rate
  • [tex]t[/tex] is the time

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

[tex]30=10e^{2r}\\\\3=e^{2r}\\\\r=\frac{In \ 3}{2}\\\\=0.54931[/tex]

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

[tex]P_t=P_oe^{rt}\\\\=10e^{6\times \frac{In \ 3}{2}}\\\\=270\ grams[/tex]

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

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