Compare the three functions. select the true statement:
[tex]\begin{gathered} F(x)=10x \\ G(x)=5^x \\ H(x)=4x^2+5x \end{gathered}[/tex]
Considering the three (3) function above, the values of x increase by positive approahes
[tex]\begin{gathered} \text{when x = 1} \\ f(x)=10x \\ f(1)=10(1)=10 \\ g(x)=5^x \\ g(1)=5^1=5 \\ h(x)=4x^2+5x \\ h(1)=4(1)^2+5(1)=4_{}+5=9 \end{gathered}[/tex]
As x value increases positively , try x = 2:
[tex]\begin{gathered} \text{when x = }2 \\ f(x)=10x \\ f(2)=10(2)=120 \\ g(x)=5^x \\ g(2)=5^2=25 \\ h(x)=4x^2+5x \\ h(2)=4(2)^2+5(2)=16_{}+10=26 \end{gathered}[/tex]
As x value increases positively , try x = 3:
[tex]\begin{gathered} \text{when x = }3 \\ f(x)=10x \\ f(3)=10(3)=30 \\ g(x)=5^x \\ g(3)=5^3=125 \\ h(x)=4x^2+5x \\ h(3)=4(3)^2+5(3)=36_{}+15=51 \end{gathered}[/tex]
From the third sequence , the exponential function tend to have increase beyong other two function,
Therefore the fourth statement seems true, as x approahes the positive infinity, the exponential function will exceed both the linear and and quadratic function.
Hence the correct answer is Option D
