Two functions are shown below.

f(x) = 1/2 • 2^x

g(x) = 5x + 2

What is the largest integer value of x such that f(x) ≤ g(x)?

looking for step by step

x = 6

Step-by-step explanation:

As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.

For small values of x, we have that f(x) < g(x). For example:

f(1) = 1/2 * 2 = 1

g(1) = 5*1 + 2 = 7

f(2) = 1/2 * 4 = 2

g(2) = 5*2 + 4 = 14

So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.

For x = 5, we have:

f(5) = 1/2 * 32 = 16

g(5) = 5*5 + 4 = 29

For x = 6, we have:

f(6) = 1/2 * 64 = 32

g(6) = 5*6 + 4 = 34

For x = 7, we have:

f(7) = 1/2 * 128 = 64

g(7) = 5*7 + 4 = 39

So the largest integer value of x for f(x) ≤ g(x) is x = 6.

Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation:

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.