For questions 1 and 2 graph the exponential function: 1. y=3^x 2. y=2(4.5)^x
2 answers:
First, we should know exponential formula, for example exp (LnA) =A, for all A>0, and as for logarythm, LnA^p=pLnA, for all A>0, and for all value of p
so y=3^x=exp[Ln(3^x)]=exp(xLn3), let's search the graph of f(x)=exp(xLn3) f is defined in R, and its teminals limits are 0, and + infinity, f' (x) = Ln3.exp(xLn3), it is positif for all value of x, the function is strictly increasing, f(0)=Ln3, please look at the figure 1
the same method with y=2(4.5)^x, we find y=exp[Ln (2(4.5)^x)]=
exp[Ln (2) +Ln(4.5)^x)], because (LnAB=LnA + LnB), so y=2.exp[Ln(4.5)^x)]=2.exp(x[Ln(4.5)]), which domain is R, nd its teminals limits are 0, and + infinity, f' (x)=2.Ln(4.5) exp(x[Ln(4.5)]), which is positif for all value of x, the function is strictly increasing,and then f(0)=2Ln(4.5)
please look the figure 2
so y=3^x=exp[Ln(3^x)]=exp(xLn3), let's search the graph of f(x)=exp(xLn3) f is defined in R, and its teminals limits are 0, and + infinity, f' (x) = Ln3.exp(xLn3), it is positif for all value of x, the function is strictly increasing, f(0)=Ln3, please look at the figure 1
the same method with y=2(4.5)^x, we find y=exp[Ln (2(4.5)^x)]=
exp[Ln (2) +Ln(4.5)^x)], because (LnAB=LnA + LnB), so y=2.exp[Ln(4.5)^x)]=2.exp(x[Ln(4.5)]), which domain is R, nd its teminals limits are 0, and + infinity, f' (x)=2.Ln(4.5) exp(x[Ln(4.5)]), which is positif for all value of x, the function is strictly increasing,and then f(0)=2Ln(4.5)
please look the figure 2
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Answer:
0.52763 is the probability that the time between the next two calls will be 54 seconds or less.
0.19285 is the probability that the time between the next two calls will be greater than 118.5 seconds.
Step-by-step explanation:
We are given the following information in the question:
The time between telephone calls to a cable television service call center follows an exponential distribution with a mean of 1.2 minutes.
The distribution function can be written as:
The probability for exponential distribution is given as:
a) P( time between the next two calls will be 54 seconds or less)
0.52763 is the probability that the time between the next two calls will be 54 seconds or less.
b) P(time between the next two calls will be greater than 118.5 seconds)
0.19285 is the probability that the time between the next two calls will be greater than 118.5 seconds.
Answer:
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Step-by-step explanation:
Let ,
, and
be scalars such that:
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The question states that . In other words:
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Make use of the fact that whereas
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The question also states that the scalar multiple here is positive. Hence, .
Therefore:
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could also be expressed in terms of
and
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Equate the two expressions and solve for and
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Hence:
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