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Find the equation of the exponential function represented by the table below:

Find the equation of the exponential function represented by the table below:-example-1

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Writing an Exponential Function given the Table

Answer:


y = 0.1(4)^x

Explanation:

Given:


&x &y \\ &0 &0.1 \\ &1 &0.4 \\ &2 &1.6 \\ &3 &6.4

The most basic form to write an exponential function is
y = ar^x. Where
a is
y when
x = 0. We can see from the given Table of Values that at
x = 0,
y = 0.1. So,
a = 0.1. The
r is the common ratio and can be calculated by
(y_(n))/(y_(n -1))\\, where
y_n is
y when
x = n.

Solving for the Common Ratio:


r = (y_(n))/(y_(n-1)) \\ r = (y_2)/(y_(2-1)) \\ r = (y_2)/(y_1) \\r = (1.6)/(0.4) \\ r = 4

Now we know what
r and
a are. We can finally write the equation of the exponential function depicted by the table.

The equation is
y = 0.1(4)^x

User Windsting
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