Identify the type of function represented by f(x)=3•(0.5)^x
2 answers:
Answer: B. Exponential decay
Step-by-step explanation:
Let x = independent variable .
The linear function is given by : , where m= slope or rate of change of y with respect to x and c = constant represents the initial value of function.
When m < 0 , then we call it decreasing linear function
When m > 0 , then we call it decreasing linear function or equation.
When m = 0 , then we call it constant function .
The exponential function is given by : , where a is the initial value of function and b is the multiplicative growth / decay rate.
When b<1 , then we call it exponential decay function.
When b>1 , then we call it exponential growth function.
Given function:
This function is exponential decay function where b= 0.5<1 .
Hence, the correct answer is B. Exponential decay.
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Answer : The incorrect step is, (A) step 1: -10 + 6x > 8
Step-by-step explanation :
The given expression is:
Now solving this expression step by step.
First -4 distributed over parentheses.
Now solving bracket term, we get:
Now taking like terms together, we get:
Now multiplying this expression by (-1), we get:
Thus, the incorrect step is, (A) step 1: -10 + 6x > 8
Answer:
The probability that at most 50 say that they drink coffee during exam week is 0.166.
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of college students who prefer to drink more coffee during the exams week.
The probability of the random variable <em>X</em> is <em>p</em> = 0.67.
A random sample of <em>n</em> = 80 college students are selected.
The response of every students is independent of the others.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 80 and <em>p</em> = 0.67.
But the sample selected is too large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
Check the conditions as follows:
Thus, a Normal approximation to binomial can be applied.
The mean of the distribution of <em>X</em> is:
The standard deviation of the distribution of <em>X</em> is:
A Normal distribution is a continuous distribution. So, the probability at a point cannot be computed for the Normal distribution. To compute the probability at a point we need to apply the continuity correction.
Compute the probability that at most 50 say that they drink coffee during exam week as follows:
Apply continuity correction:
*Use a <em>z</em>-table for the probability.
Thus, the probability that at most 50 say that they drink coffee during exam week is 0.166.