Answered

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Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 3)(0,3) and (4,48).

Sagot :

sqdancefan

Answer:

  y = 3(2^x)

Step-by-step explanation:

Put the given point values in the equation and solve for 'a' and 'b'.

  3 = a(b^0) = a . . . . . for x=0, y=3

The y-intercept has given us the value of 'a'.

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The other point will tell us 'b'.

  48 = a(b^4) = 3(b^4) . . . . . for x=4, y=48

  16 = b^4 . . . . . . . . . . . . . . . divide by 3

  2^4 = b^4   ⇒   b = 2

The exponential function is ...

  y = 3(2^x)

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Additional comment

We can use roots to find b:

  16^(1/4) = (b^4)^(1/4) = b

  2 = b . . . . your calculator can do this, or √(√16) = 16^(1/4) = 2.

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