Question

The value of the function f(x) is 600 when x=0 and decreases by 9% for every one-unit increase in x. Complete the equation that represents the function f(x)

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Answer 1

f(x) = 600 * 1.09^x

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the equation that represents the function f(x) given the provided information, we can start by setting up the equation using the given initial value and rate of decrease.

The function f(x) decreases by 9% for every one-unit increase in x. This means that for every one-unit increase in x, the value of f(x) is multiplied by (100% - 9%) = 91%.

Since the initial value of f(x) is 600 when x=0, we can construct the equation as follows:

f(x) = 600 * (0.91)^x

The exponent x represents the number of one-unit increases from x=0. By multiplying the initial value of 600 by (0.91)^x, we account for the decrease of 9% for every one-unit increase in x.

Thus, the equation that represents the function f(x) is f(x) = 600 * (0.91)^x.

Answer 3

[AI-generated answer — Explain Bot]

To solve this problem, we need to find the equation that represents the function f(x) given the provided information. Let's break down the problem step by step.

We know that the value of the function f(x) is 600 when x = 0. This gives us the starting point for our function.

Next, we are given that the function decreases by 9% for every one-unit increase in x. This means that for every unit increase in x, the value of f(x) decreases by 9%.

To incorporate this decrease into our equation, we can use the concept of a percent decrease. A percent decrease is calculated by subtracting the percentage decrease from 100% and then multiplying it by the original value.

In this case, the original value is 600, and the percentage decrease is 9%. So, the calculation for the value of f(x) when x is increased by one unit can be written as:
f(x + 1) = 600 - (9% * 600)
Simplifying this equation gives us:
f(x + 1) = 600 - 0.09 * 600
f(x + 1) = 600 * (1 - 0.09)
f(x + 1) = 600 * 0.91

Now, we have the equation to find the value of f(x + 1) in terms of the original value of f(x). We can use this equation to continue finding the values of f(x) as x increases by one unit.

Therefore, the equation that represents the function f(x) can be written as:
f(x) = 600 * (0.91)^x

In this equation, x represents the number of units by which x has increased from its initial value of 0, and f(x) represents the value of the function at that particular x value.

I hope this explanation helps! Let me know if you have any further questions.