Answer:
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<h3>
Answer: D) The y intercept is (0,1)</h3>
This can be confirmed by plugging x = 0 into the function to find that...
y = (1/2)^x
y = (1/2)^0
y = 1
Recall that any nonzero value to the 0th power leads to 1. So we can say x^0 = 1 as long as x is not zero.
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Extra info (optional section):
- We can rule out choice A because negative x values work in the domain. For instance, if x = -1, then it leads to y = (1/2)^x = (1/2)^(-1) = 2. The negative exponent will apply the reciprocal operation to the base fraction.
- Choice B can also be ruled out because the range is y > 0. Or you could note that it is possible to get positive y values smaller than 1/2. Try x = 2 and you'll see it leads to y = 1/4 which is not greater than 1/2.
- Choice C is false as well. The function f(x) = (1/2)^x is decreasing throughout the domain. A graph visually would show this due to it going downhill when moving from left to right. A table of values is a non-visual way to see we have a decreasing function. The table would show that y decreases when x increases.
<span>17−2p=4p+5
Add 2p to both sides
17=6p+5
Subtract 5 from both sides
12=6p
Divide 6 on both sides
Final Answer: 2=p</span>
What is the equivalent monthly interest rate?
If 23% is compounded each month, there will be 12 intervals and then the monthly rate is:
23 ÷ 12 = 1.92 %
If 23% is compounded annually, then the monthly rate would be:
Rate = (1 + 23%)⁰°⁸³³ (power is 0.833 or 1/12)
= 1.23⁰°⁸³³ (power is 0.833 or 1/12)
= 1.0174 - 1 x 100
= 1.74 %
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