Question

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Answer 1

The equation of the exponential function will be:

• 
  `y\:=\:10\cdot \left((1)/(5)\right)^x`

Explanation:

The general exponential function is defined as

y = abˣ

Here,

• a is the initial value and b is the growth factor

From the table, it is clear that the y-intercept is (0, 10). Note that the y-intercept can be determined by setting x=0 and solving for y.

here

at x=0, y=10

so a = 10

If we check the y-values, it is clear that every next value of y can be obtained by multiplying the previous y-value by 1/5.

In other words, the common multiplier = b = 1/5

Thus, the equation becomes

`y\:=\:10\cdot \left((1)/(5)\right)^x`

Thus, the equation of the exponential function will be:

• 
  `y\:=\:10\cdot \left((1)/(5)\right)^x`