What is the general form of an exponential function? What does each of the values represent?
Initial amount: 1 Growth factor: 1.4
Practice makes perfect
We want to identify the initial amount a and the growth factor b in the given exponential function. To do so, let's first recall the general form of an exponential growth function.
f(t)= a * b^t, where a>0 and b>1
Here, a is the initial amount and the base b is the growth factor, which equals 1 plus the percent rate of change expressed as a decimal. Let's now consider the given function.
f(t) = 1.4^t = 1 * 1.4^t
We see that a= 1 and b= 1.4. Therefore, the initial amount is 1 and the growth factor is 1.4.
