Question

A 5 inch tall bamboo shoot doubles in height every 3 days. If the equation y=ab^x, where the x is the number of doubling periods, represents the height of the bamboo shoot, what are the values of a and b?

Answer 1

In real-world scenarios, exponential equations y = ab^x can represent the following:
a: Your initial input, aka the initial height/money/population to base your equation off of.
b: Your increase; by how much your input will exponentially grow. 2 is doubling, 3 is tripling, and so on.
x: The time period in which your input increases.

So, plugging in 5 for a, and 2 for b, we get y = 5*2^x. Notice that we didn't have to use "every 3 days" for this equation, because "x is the number of doubling periods". In other words, x represents every 3 days.