Given the functions f, left bracket, x, right bracket, equals, 4, x, to the power 5f(x)=4x
5
and g, left bracket, x, right bracket, equals, 7, dot, 3, to the power xg(x)=7⋅3
x
, which of the following statements is true?
Answer
Multiple Choice Answers
f, left bracket, 7, right bracket, is greater than, g, left bracket, 7, right bracketf(7)>g(7)
f, left bracket, 7, right bracket, equals, g, left bracket, 7, right bracketf(7)=g(7)
f, left bracket, 7, right bracket, is less than, g, left bracket, 7, right bracketf(7)<g(7)
To determine which statement is true, we need to evaluate f(7) and g(7) and compare the results.
First, let's evaluate f(7):
f(x) = 4x^5
f(7) = 4(7)^5 = 4(16807) = 67228
Next, let's evaluate g(7):
g(x) = 7.3^x
g(7) = 7.3^7 = 7(2187) = 15309
Comparing the two values, we can see that f(7) is greater than g(7).
Therefore, the correct statement is: f(7) > g(7).
To determine which of the statements is true, we need to evaluate f(7) and g(7) and compare the values.
Let's start with f(x) = 4x^5. To find f(7), substitute x = 7 into the function:
f(7) = 4(7)^5
f(7) = 4 * 16807
f(7) = 67228
Now let's evaluate g(x) = 7 * 3^x. To find g(7), substitute x = 7 into the function:
g(7) = 7 * 3^7
g(7) = 7 * 2187
g(7) = 15309
Comparing the values, f(7) = 67228 and g(7) = 15309.
Since 67228 is greater than 15309, the statement "f(7) is greater than g(7)" is true. Therefore, the correct answer is:
f(7) > g(7)
To determine which of the following statements is true, we can substitute x = 7 into both functions f(x) and g(x) and compare the results.
Let's start with f(x) = 4x^5:
f(7) = 4(7)^5 = 4(16807) = 67228
Now, let's evaluate g(x) = 7.3^x:
g(7) = 7.3^7 ≈ 7(2187) ≈ 15309
Comparing the values, we can see that f(7) = 67228 is greater than g(7) ≈ 15309.
So, the correct statement is:
f(7) > g(7)