Question

Two functions are shown below:

f(x) = 15 + (1.1)x and g(x) = 115 + 1.1x. For what integer value of x does the value of f(x) first exceed the value of g(x)?
A) x = 5
B) x = 10
C) x = 15
D) x = 20

Answer 1

By testing the provided options, it is found that the function f(x) exceeds g(x) for the first time at the integer value x = 20, making option D the correct answer.

Step-by-step explanation:

The student's question involves finding the integer value of x where the function f(x) first exceeds the function g(x). The functions given are f(x) = 15 + (1.1)x and g(x) = 115 + 1.1x.

To solve this, we need to find the smallest integer x for which f(x) > g(x). We can set up an inequality like so:

15 + (1.1)x > 115 + 1.1x

This inequality does not have an analytical solution, so we must solve it by testing the integer values of x starting from the smallest possible value and continuing until we find the one where f(x) exceeds g(x).

Testing the options provided:

• f(5) = 15 + (1.1)5 compared to g(5) = 115 + 1.1(5)
• f(10) = 15 + (1.1)10 compared to g(10) = 115 + 1.1(10)
• f(15) = 15 + (1.1)15 compared to g(15) = 115 + 1.1(15)
• f(20) = 15 + (1.1)20 compared to g(20) = 115 + 1.1(20)

Through trial, we find that f(x) exceeds g(x) at x = 20, making option D the correct answer.