At t=2 hours, the populations of bacteria colony was 456 and at 4.2 hours, the population was 988. at what time can we expect the population to be 8700?

  10.4 hours

Step-by-step explanation:

It is convenient to write the exponential growth function in these terms:

  population = (initial value)·((value at later time)/(initial value))^exponent

where ...

  exponent = (t - (initial time))/(time difference to later time)

Here, we have ...

So, the exponential function is ...

  p(t) = 456·(988/456)^((t-2)/2.2)

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We can find t for p(t) = 8700 a couple of ways. My favorite is to use a graphing calculator to find t such that ...

  p(t) -8700 = 0

This shows t ≈ 10.4 hours.

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Alternatively, you can solve the equation using algebra.

  8700 = 456·(988/456)^((t-2)/2.2)

  8700/456 = (988/456)^((t-2)/2.2) . . . . . . . . . . .divide by 456

  log(8700/456) = (t -2)/2.2 · log(988/456) . . . . taking logs

  2.2·log(8700/456)/log(988/456) = t -2 . . . . . . multiply by the inverse of the coefficient of t

  t = 2 + 2.2(log(8700/456)/log(988/456)) ≈ 10.389774

We can expect the population to be 8700 at 10.4 hours.

5

step-by-step explanation:

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.