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Ainat [17]
3 years ago
9

Which of the following graphs of exponential functions corresponds to a geometric sequence with a first term of 4 and a ratio of

1/2?

Mathematics
2 answers:
bogdanovich [222]3 years ago
6 0
"Graph E" is the one among the following choices given in the question that graphs <span>of exponential functions corresponds to a geometric sequence with a first term of 4 and a ratio of 1/2. The correct option among all the options that are given is the fifth option. I hope the answer has actually come to your help.</span>
ser-zykov [4K]3 years ago
3 0

Answer: graph E.


A geometric sequence can be written as:

a_{n} = a_{1} \cdot r^{(n - 1)}

where:

a₁ = first term = 4

r = ratio = 0.5


Substituting the numbers, we have:

a_{n} = 4 \cdot (\frac{1}{2})^{n-1}

or else

f(x) = 4 \cdot (\frac{1}{2})^{x - 1}


This is an exponential function with base less than 1. Therefore, we can exclude graph C (which depicts a linear function), and graphs A and D (which depict an exponential function with base greater than 1).


In order to choose between graph B and E, let's evaluate the function in two different points:

f(1) = 4 \cdot (\frac{1}{2})^{1 - 1} = 4

f(2) = 4 \cdot (\frac{1}{2})^{2 - 1} = 4 \cdot \frac{1}{2} = 2


Therefore, we need to look for the graph passing through the points (1, 4) and (2, 2). That is graph E.




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