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ACT Math : Graphing

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Example Questions

Example Question #12 : How To Graph An Exponential Function

If the functions

$f(x) = e^{x}+ 9$ $\displaystyle f(x) = e^{x}+ 9$

$g(x) = 4e^{x}- 7$ $\displaystyle g(x) = 4e^{x}- 7$

were graphed on the same coordinate axes, what would be the $\displaystyle x$-coordinate of their point of intersection?

Round to the nearest tenth, if applicable.

Possible Answers:

The graphs of $\displaystyle f$ and $\displaystyle g$ would not intersect.

2.7 $\displaystyle 2.7$

5.3 $\displaystyle 5.3$

14.3 $\displaystyle 14.3$

1.7 $\displaystyle 1.7$

Correct answer:

1.7 $\displaystyle 1.7$

Explanation:

We can rewrite the statements using $\displaystyle y$ for both f(x) $\displaystyle f(x)$ and g(x) $\displaystyle g(x)$ as follows:

$y = e^{x}+ 9$ $\displaystyle y = e^{x}+ 9$

$y = 4e^{x}- 7$ $\displaystyle y = 4e^{x}- 7$

To solve this, we can set the expressions equal, as follows:

$4e^{x}- 7 = e^{x}+ 9$ $\displaystyle 4e^{x}- 7 = e^{x}+ 9$

$4e^{x}- 7 - e^{x} + 7 = e^{x}+ 9 - e^{x} + 7$ $\displaystyle 4e^{x}- 7 - e^{x} + 7 = e^{x}+ 9 - e^{x} + 7$

$3e^{x} = 16$ $\displaystyle 3e^{x} = 16$

$3e^{x}\div 3 = 16 \div 3$ $\displaystyle 3e^{x}\div 3 = 16 \div 3$

$e^{x} = \approc 5.3333$ $\displaystyle e^{x} = \approc 5.3333$

$x \approx \ln 5.333 \approx 1.7$ $\displaystyle x \approx \ln 5.333 \approx 1.7$

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ACT Math : Graphing

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #12 : How To Graph An Exponential Function

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