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Which of the following functions has the largest value when [tex]$x = 5$[/tex]?

[tex]
\begin{array}{l}
p(x) = 2x^2 + 4x + 11 \\
h(x) = 4^x \\
s(x) = 10x
\end{array}
[/tex]


Sagot :

To determine which of the following functions has the largest value when [tex]\( x = 5 \)[/tex]:

[tex]\[ \begin{align*} p(x) &= 2x^2 + 4x + 11 \\ h(x) &= 4^x \\ s(x) &= 10x \\ \end{align*} \][/tex]

Step-by-step evaluation of each function at [tex]\( x = 5 \)[/tex]:

1. Calculate [tex]\( p(5) \)[/tex]:

[tex]\[ p(5) = 2(5)^2 + 4(5) + 11 \][/tex]

First, calculate [tex]\( 2(5)^2 \)[/tex]:

[tex]\[ 2(5)^2 = 2(25) = 50 \][/tex]

Next, calculate [tex]\( 4(5) \)[/tex]:

[tex]\[ 4(5) = 20 \][/tex]

Add these results together along with the constant 11:

[tex]\[ p(5) = 50 + 20 + 11 = 81 \][/tex]

2. Calculate [tex]\( h(5) \)[/tex]:

[tex]\[ h(5) = 4^5 \][/tex]

Calculate [tex]\( 4^5 \)[/tex] through exponentiation:

[tex]\[ 4^5 = 1024 \][/tex]

3. Calculate [tex]\( s(5) \)[/tex]:

[tex]\[ s(5) = 10(5) \][/tex]

Calculate [tex]\( 10(5) \)[/tex]:

[tex]\[ 10(5) = 50 \][/tex]

Summary of the values calculated at [tex]\( x = 5 \)[/tex]:

[tex]\[ \begin{align*} p(5) &= 81 \\ h(5) &= 1024 \\ s(5) &= 50 \\ \end{align*} \][/tex]

To find the largest value, compare these results:

[tex]\[ p(5) = 81, \quad h(5) = 1024, \quad s(5) = 50 \][/tex]

Among the values [tex]\( 81 \)[/tex], [tex]\( 1024 \)[/tex], and [tex]\( 50 \)[/tex], the largest value is [tex]\( 1024 \)[/tex].

Thus, the function with the largest value at [tex]\( x = 5 \)[/tex] is [tex]\( h(x) = 4^x \)[/tex].