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LenaWriter [7]
3 years ago
5

Which exponential function goes through the points (1, 8) and (4, 64)?

Mathematics
1 answer:
Mama L [17]3 years ago
6 0
An exponential function can be expressed as:

y=ab^x  we have two points so we can solve

64/8=(ab^4)/(ab^1)

8=b^3

2=b, now we have:

y=a(2^x), using point (4,64)

64=a(2^4)

64=16a

4=a so

y=4(2^x)
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Answer:

Option A

Step-by-step explanation:

We need to find two expressions that, when simplified, give the same results.

1) First, simplify the expression stated in the question. Multiply each of the terms in the parentheses by the number that is next to them. This would mean you have to multiply both 9x and -6 by \frac{2}{3}. You also have to multiply \frac{1}{2}x and -\frac{1}{2} by 4. Then, simplify.

\frac{2}{3}(9x-6) + 4 (\frac{1}{2} x - \frac{1}{2})\\\frac{18}{3}x- \frac{12}{3} + \frac{4}{2}x -\frac{4}{2} \\6x - 4 + 2x - 2

2) Now, combine the like terms.

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So, we need to find which of the expressions listed equal 8x - 6.

3) Let's try option A. Do the same as before. Multiply each of the terms in the parentheses by the number that is next to them. So, multiply 4x and -12 by \frac{3}{4}. Also, multiply 30x and 18 by \frac{1}{6}. Then, combine like terms and simplify.

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This also equals 8x - 6. Therefore, option A is the answer.

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