9514 1404 393
Answer:
(d) y = 2×7^x
Step-by-step explanation:
If you try x=2 in each of the expressions, you find only one of the gives 98 as the value.
a) 14^2 = 196
b) 7×2^2 = 28
c) 2^(7×2) = 2^14 = 16,384
d) 2×7^2 = 2×49 = 98 . . . . . . . correct answer choice
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Alternatively, you can recognize that the x-values in the given (x, y) pairs differ by 1, so the ratio of y-values will be the base of the exponential term:
98/14 = 7
so you're looking for something of the form 7^x. That would be ...
y = 2×7^x
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In more general terms, consider
y = ab^x
If you have x=1 and x=2, then this will be ...
y1 = ab^1 = ab
y2 = ab^2
Dividing the second by the first gives ...
y2/y1 = (ab^2)/(ab) = b . . . . . . . general solution when x-values differ by 1
98/14 = b = 7
From the x=1 case, we have ...
14 = 7a ⇒ a = 2
y = 2·7^x
