Question

Which of the following exponential equations could be represented by the table below?
mc027-1.jpg mc027-2.jpg3 mc027-3.jpg2 mc027-4.jpg1 0 1 2 3 4 5
mc027-5.jpg 2.0014 2.0041 2.0123 2.037 2.111 2.333 3 5 11
mc027-6.jpg
mc027-7.jpg
mc027-8.jpg
mc027-9.jpg

Answer 1

The values approach 2 for large negative x, so the horizontal asymptote is y = 2. Write y = 2 + A·r^x.

From x = 4 and x = 5: (y5 − 2)/(y4 − 2) = (11 − 2)/(5 − 2) = 9/3 = 3, so r = 3.
Then y4 − 2 = A·3^4 = 3, so A = 3/81 = 1/27.

Thus y = 2 + (1/27)·3^x, which is equivalently y = 2 + 3^{x−3}.