Question

You start a bacterial colony and notice that it quadruples each day. What does the term 65 mean in the exponential function y=65*4^x?

Answer 1

the number of bacteria you started with

Answer 2

Answer: C) The number of bacteria you started with

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Reason:

The start point occurs at x = 0, since negative time values do not make sense. In other words, a negative number of days isn't possible.

Plug x = 0 into the function to find that...

y = 65*4^x

y = 65*4^0

y = 65*1

y = 65

Recall that raising any nonzero number to the zeroth power gives 1 (i.e. x^0 = 1 where x is any number but zero)

We've shown that x = 0 leads to y = 65.

That number out front (65) is the amount of bacteria at the start, to confirm the answer above.

In general, y = a*b^x will have "a" as the starting amount. We have a = 65 and b = 4 in this case. The "b" term is tied closely to the growth rate.