Mike forgot to replace the cap on a bottle of room freshener. The room freshener began to evaporate at the rate of 15% per day.
If the original amount of room freshener in the bottle was 40 grams, which of the following graphs best represents the amount of room freshener f(x) that would remain in the bottle after x days?
graph of function f of x equals 30 multiplied by 0.88 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis
graph of function f of x equals 50 multiplied by 0.82 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis
graph of function f of x equals 30 multiplied by 0.88 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis
graph of function f of x equals 50 multiplied by 0.82 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis
1 answer:
The decay rate is 100% - 15% = 75% = 0.75
The decay equation is f(x) = 40(0.75)ˣ
Where f(x) is the mass of air freshener left after x days of use
The graph of this function is given below
The correct description of the graph is statement 2:
<span>graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis</span>
The decay equation is f(x) = 40(0.75)ˣ
Where f(x) is the mass of air freshener left after x days of use
The graph of this function is given below
The correct description of the graph is statement 2:
<span>graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis</span>
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Answer:
Using the binomial distribution we can find this probability with the following excel code:
"=BINOM.DIST(30,200,0.1,TRUE)", and we got:
Using the normal approximation
We can use the continuity factor correction:
And we can use the z score formula given by:
And we got:
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
We want to find this probability;
Using the binomial distribution we can find this probability with the following excel code:
"=BINOM.DIST(30,200,0.1,TRUE)", and we got:
The other way is using the normal approximation for the binomial distribution
We need to check the conditions in order to use the normal approximation.
So we see that we satisfy the conditions and then we can apply the approximation.
If we appply the approximation the new mean and standard deviation are:
And we can use the continuity factor correction:
And we can use the z score formula given by:
And we got: