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alisha [4.7K]
2 years ago
13

Find C and a so that f(x) = CaX models the situation described. State what the variable x represents in your formula. In 2000 a

house was worth $220,000, and its value decreases by 11% each year thereafter. please help im failing ​
Mathematics
1 answer:
Nezavi [6.7K]2 years ago
8 0

Answer:

f(x) = Ca^x

x = years since 2000.

f(0) = 220000 = Ca^0 = C

f(x) = 220000a^x

f(1) = 220000(1-0.11) = 220000a^1

a = 0.89

f(x) = 220000(0.89)^x

So each year reduces by 89%

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A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that t_{\alpha/2}=2.36

Now we have everything in order to replace into formula (1):

12-2.36\frac{2.268}{\sqrt{8}}=10.108    

12+2.36\frac{2.268}{\sqrt{8}}=13.892

So on this case the 95% confidence interval would be given by (10.108;13.892)

10.108 < \mu < 13.892    

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