Question

The function f(x) = 800(1.09)5x shows the growth due to interest that Jim earns on an investment. The steps to calculate an equivalent function are shown below: [Step 1] f(x) = 800(1.09)5x [Step 2] f(x) = 800(1.095)5x [Step 3] f(x) = 800(1.5386)5x [Step 4] f(x) = 800(1.5386)x Which of the following is the first incorrect step?

Answer 1

Assuming that [Step 1] has f(x) = 800(1.09)⁵ˣ and
[Step 2] f(x) = 800(1.09⁵)⁵ˣ, the answer is Step 2. The coefficient of 5 must be taken away as dictated by the property of exponents.

Answer 2

The correct answer is: [Step 2] is the first incorrect step.

Explanation:

The given function, which is also the Step-1 in the question:

$f(x)=800(1.09)^{5x}$

Step-2:

We can bring the coefficient of the exponent 5x inside the parenthesis by using the following property of exponent:

$n(Z)^{ax} = n(Z^a)^x$

In the step-2 mentioned in the question, the aforementioned property is used incorrectly. An extra "5" has been introduced in the power in step-2, which is wrong.

Wrong step-2:

$f(x)=800(1.09^5)^{5x}$

(EXTRA) How to correct this step:

You can use the above-mentioned property, and write the following:

$f(x)=800(1.09^5)^{x}$

Hence the first incorrect step is [Step 2].