Given the functions f, left bracket, x, right bracket, equals, 5, x, to the power 4f(x)=5x
4
and g, left bracket, x, right bracket, equals, 5, dot, 2, to the power xg(x)=5⋅2
x
, which of the following statements is true?
Answer
Multiple Choice Answers
f, left bracket, 16, right bracket, is less than, g, left bracket, 16, right bracketf(16)<g(16)
f, left bracket, 16, right bracket, is greater than, g, left bracket, 16, right bracketf(16)>g(16)
f, left bracket, 16, right bracket, equals, g, left bracket, 16, right bracketf(16)=g(16)
To find the values of f(16) and g(16), we substitute x = 16 into the given functions.
For f(x) = 5x^4, we have:
f(16) = 5(16)^4 = 5(65,536) = 327,680.
For g(x) = 5⋅2^x, we have:
g(16) = 5⋅2^16 = 5(65,536) = 327,680.
Therefore, f(16) = g(16), so the correct statement is f(16) = g(16).
To determine which of the statements is true, we need to evaluate the functions f(16) and g(16) and compare the results.
Let's start with f(x) = 5x^4. To find f(16), we substitute x = 16 into the function:
f(16) = 5 * 16^4
= 5 * 65536
= 327680
Next, let's evaluate g(x) = 5 * 2^x. Similarly, we substitute x = 16 into the function:
g(16) = 5 * 2^16
= 5 * 65536
= 327680
From the calculations, we can see that f(16) equals g(16), which means the correct statement is:
f(16) = g(16)
To determine which statement is true, we need to evaluate the functions f(16) and g(16).
Let's start with f(x) = 5x^4. Plugging in x = 16, we have:
f(16) = 5(16)^4 = 5(256) = 1280.
Now let's evaluate g(x) = 5 * 2^x:
g(16) = 5 * 2^16 = 5 * 65536 = 327680.
Comparing the values, we find that f(16) = 1280, while g(16) = 327680.
Therefore, the correct statement is:
f(16) is less than g(16) (f(16) < g(16)).