State the starting value a the growth factor b and the perce

State the starting value a, the growth factor b, and the percentage growth rate r for the given exponential function. Q=92^t

Solution

We know that an exponential growth or decay function is a function that grows or shrinks at a constant percent growth rate. Its equation can be written in the form

f(x) = a(1+r)^x or    f(x ) = ab^x   where b = 1+r

Where

·         a is the initial or starting value of the function;

·         r is the percent growth or decay rate, written as a decimal; and

·         b is the growth factor or growth multiplier. Since powers of negative numbers behave strangely, we limit b to positive values.

Here, the growth function is Q = (9.2)^t = 1*(9.2)^t . Thus, the starting value i.e.   a = 1, the growth factor, i.e. b = 9.2 and the percentage growth rate i.e. r = b – 1= 9.2 – 1 = 8.2