Tell whether the function represents exponential growth or exponential decay. Then graph the function. f(x)=(0.25)^{x}

Question
Exponential growth and decay
asked 2021-02-11
Tell whether the function represents exponential growth or exponential decay. Then graph the function. \(\displaystyle{f{{\left({x}\right)}}}={\left({0.25}\right)}^{{{x}}}\)

Answers (1)

2021-02-12
Step 1 Given: \(\displaystyle{f{{\left({x}\right)}}}={\left({0.25}\right)}^{{{x}}}\) Step 2 Thefunction represents exponential decay because it has the form \(\displaystyle{y}={a}{b}^{{{x}}}\) \text{with} a>0,0\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&-{2}&-{1}&{0}&{1}&{2}&{3}\backslash{h}{l}\in{e}{y}&{16}&{4}&{1}&{0.25}&{0.0625}&{0.016}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\) Step 3 In order to graph the function, we build a table of values: \(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&-{2}&-{1}&{0}&{1}&{2}&{3}\backslash{h}{l}\in{e}{y}&{16}&{4}&{1}&{0.25}&{0.0625}&{0.016}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\) Step 4 We plot the points from the table, then draw a smooth curve that begins on the right, just above the x-axis, passes through the plotted points and moves up to the left: <img src="https://q2a.s3-us-west-1.amazonaws.com/dev/19610300571.jpg PSZ
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