40Points? CORRECT answer please

Mathematics

1 answer:

irina [24]3 years ago

3 0

Answer:

Step-by-step explanation:

$f(t)=2(0.4)^t$

f(-2) → put t = -2 to the equation of the function:

$f(-2)=2(0.4)^{-2}=2\left(\dfrac{4}{10}\right)^{-2}=2\left(\dfrac{2}{5}\right)^{-2}$

Use $a^{-n}=\left(\dfrac{1}{a}\right)^n$

$f(-2)=2\left(\dfrac{5}{2}\right)^2=2\left(\dfrac{25}{4}\right)=\dfrac{25}{2}=12.5$

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now, for the Blue one, say let's use hmmm it passes through (0,2) and (1.6)

$\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{6}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-2}{1-0}\implies \cfrac{4}{1}\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=4(x-0) \\\\\\ y-2=4x\implies \blacktriangleright y=4x+2 \blacktriangleleft$