hi I am new please help me with my homework as soon as possible please

Question

The cells of a certain culture of bacteria triple every 2 minutes. If there are 40 cells in the beginning, in how many minutes will there be more than 9500 cells?

  A.) 10 min

  B.) 4 min

  C.) 5 min

  D.) 11 min

 

Answer 1

The function would be f(x) = 40(3)^t/2 where "t" is time in minutes.

To find when you reach 9500 cells, make f(x) = 9500 and solve for "t":

9500 = 40(3)^t/2

9500/40 = 3^t/2

237.5 = 3^t/2)

log₃(237.5) = log₃(3^t/2)

4.979161147 = t/2(log₃(3))

4.979161147 = t/2

t = 2(4.979161147) = 9.96 minutes ≈ 10 minutes