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Semmy [17]
1 year ago
15

See question in screenshot below.

Mathematics
1 answer:
alexgriva [62]1 year ago
3 0

The equation of the transformation of the exponential function <em>y</em> = 2ˣ in the form <em>y</em> = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is <em>y</em> = (-2)·2ˣ + 3

<h3>What is an exponential equation?</h3>

An exponential equation is an equation that has exponents that consists of variables.

The given equation is <em>y</em> = 2ˣ

The equation for the transformation is; <em>y</em> = A·2ˣ + k

The points on the graphs are;

(0, 1), (1, -1) and (2, -5)

Plugging the <em>x </em>and <em>y</em>-values to find the value <em>A</em> and <em>k</em> gives  the following simultaneous equations;

When <em>x</em> = 0, <em>y</em> = 1, therefore;

1 = A·2⁰ + k = A + k

1 = A + k...(1)

When <em>x</em> = 1, <em>y</em> = -1, which gives;

-1 = A·2¹ + k

-1 = 2·A + k...(2)

Subtracting equation (1) from equation (2) gives;

-1 - 1 = 2·A - A + k - k

-2 = A

1 = A + k, therefore;

1 = -2 + k

k = 2 + 1 = 3

k = 3

Which gives;

y = -2·2ˣ + 3 = 3 - 2·2ˣ

Learn more about the solutions to simultaneous equations here:

brainly.com/question/26310043

#SPJ1

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