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39 votes
39 votes
Can someone help me please :)

Can someone help me please :)-example-1
User Jansanchez
by
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1 Answer

16 votes
16 votes

9514 1404 393

Answer:

(d) y = 2×7^x

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

User Kevinhyunilkim
by
2.8k points