First, we need to solve the differential equation.
This a separable ODE. We can rewrite it like this:
Now we integrate both sides.
We get:
When we solve for y we get our solution:
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.
Answer:
The sampling option Hamden city's police department needs to choose is to select a random sample of 10% of all taxpayers.
Since the Hamden city’s police department needs to choose whether to build a new addition to the police station or to buy new squad cars. And it needs money to choose any of these options. The money usually comes from the packets of taxpayers. Therefore, it would be appropriate to take a random sample of 10% of all taxpayers.
Answer:
$277.91
Step-by-step explanation:
"The 26-week average of the two highest salaried quarters of the year leading to her application" would be the average of $13,500 and $12,775, or
$13,500 + $12,775
---------------------------- = $13137.50
2
Dividing this by 26 weeks (equivalent to 6 months), we get $505.29.
Nancy's weekly employment benefit would be 55% of that, or $277.91.
No, having the greater rate of change does not mean a function will necessarily reach an output with the smallest input. It also depends on the initial values of the functions. If Jeremy's aunt lives closer to school, Jeremy's rate of change is smaller, but he could still get to school before Amy.
Analysis to obtain the function that models the polulaiton ob bees:
1) First year 9,000 bees
2) Second year: decrease 5% => 9,000 - 0.05* 9,000 = 9,000 * (1 - 0.05) = 9,000 * 0.95
3) Every year the population decreases 5% => 9,000 * 0.95)^ (number of years)
4) if you call x the number of years, and f(x) the function that represents the number of bees, then: f(x) = 9,000 (0.95)^ x.
Analysis of the statements:
<span>1) The
function f(x) = 9,000(1.05)x represents the situation.
FALSE: WE DETERMINED IT IS f(x) = 9,000 (0.95)^x
2) The function
f(x) = 9,000(0.95)x represents the situation.
TRUE: THAT IS WHAT WE OBTAINED AS CONCLUSION OF THE PREVIOUS ANALYSIS.
3) After 2 years, the farmer
can estimate that there will be about 8,120 bees remaining.
Do the math:
f(2) = 9,000 * (0.95)^2 = 9,000 * 0,9025 = 8,122
So, the statement is TRUE
4) After 4
years, the farmer can estimate that there will be about 1,800 bees
remaining.
f(4) = 9,000 * (0.95)^4 = 9,000 * 0.81450625 = 7,330
So, the statement is FALSE
5) The domain values, in the context of the situation, are
limited to whole numbers.
FALSE: THE DOMAIN VALUES ARE ALL NON NEGATIVE REAL VALUES. FOR EXAMPLE THE FUNCTION IS WELL DEFINED FOR X = 5 AND HALF
6) The range values, in the context of the
situation, are limited to whole numbers.
TRUE: THERE CANNOT BE FRACTIONS OF BEES
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