anonymous
  • anonymous
how do you find an exponential equation through the points (0,6) and (2, 9)?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
an exponential equation follows the form y = ae^x + b, where and b are some constants. To use this, we plug in known values, which will give us a system of equations. (0,6): 6 = ae^0 + b = a + b (2,9): 9 = ae^2 + b we can subtract the first one from the second to get: 3 = ae^2 - a = a(e^2 - 1), or a = 3/(e^2 - 1) and we can then plug this value of a into either equation we got first to get b. I'll plug it into the first one: 6 = a + b = (3/(e^2 - 1)) + b, or b = 6 - (3/(e^2 - 1)). Then put the values of a and b into the general form of an exponential equation y = (3/(e^2 - 1))e^x + (6 - 3/(e^2 - 1)). Plug the two initial points given to make sure the equation is correct

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