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The exponential function represented by the table can be written in the form y=ab^x. Find the values for a and b.

The exponential function represented by the table can be written in the form y=ab^x. Find the values for a and b. class=

Answer :

tаskmasters
If this function can be written in the form y = ab^x, then we see that when x is inputted as 0, y is outputted as 4. This means that
                                          4 = ab^0
                                          a = 4
The value of a is 4.
We see that when x = 1, y = 2 thus
                                           y = 4b^x
                                          2 = 4(b^1)
                                          b = 1/2
The answers are a = 4 and b = 1/2
raphealnwobi

The exponential function gotten from the table is given by y = 4(1/2)ˣ

Exponential function

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multipliers.

From the table, at point (0, 4):

  • 4 = ab⁰
  • a = 4

At point (3, 1/2):

  • y = abˣ
  • 1/2 = 4b³
  • b = 1/2

The exponential function gotten from the table is given by y = 4(1/2)ˣ

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