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Answer:
A: a = 100
B: b = 2
Step-by-step explanation:
The problem statement tells you that the population of bacteria is 100 at the start of our observation.
t = 0, f(t) = f(0) = 100
If you remember that a 0 exponent means the value is 1, then you know ...
f(0) = a·b^0 = a·1 = a
Since f(0) = 100, we know a = 100.
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An exponent signifies repeated multiplication.
We know the population at t=0 is 100. At t = 1, we are told the population doubles. That means it is multiplied by 2.
f(1) = 100·b^1 = 100·2
b^1 = 2 . . . . . . . . . . . . . . . matching parts of these expressions
b = 2 . . . . . . . . . . . . . because b^1 = b
