Question

In the equation f() = 275(1.04)ˣ, is the function increasing or decreasing, and by what percentage does it change per unit increase in the function increasing or decreasing, and by what percentage does it change per unit increase in ?

Answer 1

The given function f(x) = 275(1.04)^x is increasing. To find the percentage change per unit increase in x, compare two function values using the percentage change formula.

Step-by-step explanation:

The given function is f(x) = 275(1.04)x.

To determine if the function is increasing or decreasing, we need to observe the base of the exponent.

In this case, the base is 1.04, which is greater than 1, indicating exponential growth. Therefore, the function is increasing.

To find the percentage change per unit increase in x, we can compare two function values.

Let's consider two values, x_1 and x_2, where x_2 is one unit greater than x_1.

For x = x_1, f(x) = 275(1.04)x_1.

For x = x_2, f(x) = 275(1.04)x_2.

To find the percentage change, we can use the formula:

Percentage change = ((f(x_2) - f(x_1)) / f(x_1)) * 100%.

Substituting the values, we get:

Percentage change = ((275(1.04)x_2) - (275(1.04)x_1)) / (275(1.04)x_1) * 100%.

Simplifying further will give the exact percentage change for each unit increase in x.