Which function represents exponential decay?f(x)=1/2(2)xf(x)=3/4(-1/5)xf(x)=(7/2)xf(x)=2(2/3)x
2 answers:
Answer: The answer is (D)
Step-by-step explanation: We are to select the correct function which represents exponential decay.
We know that an exponential decay is represented by the function with base less than 1.
For example, if we consider the following exponential function:
then f(x) will show exponential growth if b > 1 and exponential decay is b < 1.
Among the given functions, represents exponential decay, because the base is 0.66, which is less than 1.
Thus, (D) is the correct option.
The graph of this resultant function is attached, which clearly represents exponential decay.
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compare the divisor x-3 with x-a which will give a=3 and then use remainder theorem.
Answer:
5.05% probability that no more than 34% had received such an email.
Step-by-step explanation:
We use the binomial approximation to the normal to solve this problem.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
In a random sample of 700 adults, what is the probability that no more than 34% had received such an email?
34% is 0.34*700 = 238
So this probability is the pvalue of Z when X = 238.
has a pvalue of 0.0505
5.05% probability that no more than 34% had received such an email.