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2 years ago

Which statements are true about exponential decay functions check all that apply

Mathematics

2 answers:

lisabon 2012 [21]2 years ago

5 0

Answer:

The correct statements are:

1) The domain is all real numbers.

4) The base must be less than 1 and greater than 0.

5) The function has a constant multiplicative rate of change.

Step-by-step explanation:

<em>Any function in the form f(x)=ab^x, where a > 0, b > 0 and b not equal to 1 is called an exponential function with base b.</em>

if b>1 then we get a exponential growth function and

We know that a exponential decay function is given as:

f(x)=ab^x with 0<b<1

Hence, the statements that are true about the exponential decay functions are:

1) The domain is all real numbers.

This statement is true since the function is defined for all the real values.

2) As the input increases, the output increases.

This statement is false since from the graph we could check that the exponential decay function decreases with the increasing value of x.

3) The graph is the same as that of an exponential growth function .

The statement is false since the graph of growth function increases with increasing x and is opposite of the decay function.

4) The base must be less than 1 and greater than 0.

This statement is true.

5) The function has a constant multiplicative rate of change.

This option is true.

Since there is a constant multiplicative rate of change (i.e. b)

melomori [17]2 years ago

3 0

This is the concept of exponential functions; The statements that are correct about the exponential decay functions are:
1. The domain is all real number
4. The base must be less than 1 and greater than 0
5. The function has a constant multiplicative rate of change

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And replacing n = 24 we got:

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Step-by-step explanation:

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Solution to the problem

For this case assuming that the random variable is X

$df = n-1$

And replacing n = 24 we got:

$df = 24-1=23$

And we notate the distribution we got: $X \sim t_{n-1}= t_{23}$

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First Question

For a better understanding of the solution provided here please find the first attached file which has the diagram of the the isosceles trapezoid.

We dropped perpendiculars from C and D to intersect AB at Q and P respectively.

As can be seen in $\Delta BCQ$ , we can easily find the values of CQ and BQ.

Since, $Sin(75^0)=\frac{CQ}{8}$

$\therefore CQ=8\times Sin(75^0)\approx 7.73$ ft

In a similar manner we can find BQ as:

$Cos(75^0)=\frac{BQ}{8}$

$BQ\approx2.07$ ft

All these values can be found in the diagram attached.

Thus, because of the inherent symmetry of the isosceles trapezoid, PQ can be found as:

$PQ=22-(AP+QB)=22-(2.07+2.07)=17.86$

Let us now consider $\Delta AQC$

We can apply the Pythagorean Theorem here to find the length of the diagonal AC which is the hypotenuse of $\Delta AQC$ .

$AC=\sqrt{(AQ)^2+(QC)^2}=\sqrt{(AP+PQ)^2+(QC)^2}=\sqrt{(2.07+17.86)^2+(7.73)^2}\approx21.38$ feet.

Thus, out of the given options, Option B is the closest and hence is the answer.

Second Question

For this question we can directly apply the formula for the area of a triangle using sines which is as:

Area= $\frac{1}{2}$ (First Side)(Second Side)(Sine of the angle between the two sides)

Thus, from the given data,

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Therefore, Option D is the correct option.

Third Question

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Thus, from the triangle we will have:

$\frac{AB}{Sin(\angle C)}=\frac{BC}{Sin(\angle A)}$

$\frac{c}{Sin(\angle C)}=\frac{a}{Sin(\angle A)}$

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This gives $a$ to be:

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Which is not close to any of the given options.

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Please find the second attachment for a better understanding of the solution provided her.

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