Step 1 :The exponential growth function in terms of P and 0.04 is given by: \(P(t) = P \times e^{0.04t}\)
Step 2 :If $9,000 is invested, the balance after 5 years can be calculated by substituting P = 9000 and t = 5 into the exponential growth function: \(P(5) = 9000 \times e^{0.04 \times 5} = 9000 \times e^{0.2} = 9000 \times 1.22140275816 = $10992.62\)
Step 3 :To find out when an investment of $9,000 will double itself, we need to solve the equation \(9000 \times e^{0.04t} = 2 \times 9000\) for t. Simplifying, we get \(e^{0.04t} = 2\), then \(0.04t = \ln(2)\), and finally \(t = \frac{\ln(2)}{0.04} = 17.3\) years
Step 4 :\(\boxed{17.3}\) years is the time it will take for an investment of $9,000 to double itself.