Question

Arrange the following in ascending order of their values at $x=2.$

• A. $f\left(x\right)={3.7}^x$
• B. $f\left(x\right)={1.2}^x$
• C. $f\left(x\right)={2.5}^x$
• D. $f\left(x\right)=2^x$
• E. $f\left(x\right)={3.2}^x$

Answer 1

Given $f\left(x\right)$ of the form $f\left(x\right)=a^x;a>1$
For any two exponential functions $f\left(x\right)=a_1^x\&g\left(x\right)=a_2^x$ where $a_2>a_1,$ we can have the graph drawn for them as:
Clearly, for $x_i>0$
$a_2>a_1\Rightarrow a_2^{x_i}>a_1^{x_i}$
Thus, for $x=2,$ we can arrange them in ascending order as:
${1.2}^x<2^x<{2.5}^x<{3.2}^x<{3.7}^x$