Question

For the equation f(x)= 1.8(0.53)*, state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x.

-(Type an integer or a decimal.)
C=

Answer 1

I'm assuming the function is
`f(x)= 1.8(0.53)^x`.

The general form of an exponential function is
`f(x) = C\cdot a^x`.

C is the initial value, which is 1.8 in this case.

a is the decay factor, which is 0.53 in this case.

The decay factor tells you what percent remains for each unit increase in x. This decay factor tells you that 53% remains for each unit increase in x.

Here's the catch: when you describe the decay *rate*, you need to describe what has been lost. So if 53% remains, then 47% is lost for each unit increase in x.

The decay rate if 47% for each unit increase in x.

Exponential functions are calculated by what remains, but we always describe them based off of how much they've changed from 100%. A 15% rate of decay gives you a decay factor of 0.85, since 85% remains.