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4 years ago

Which is an exponential decay function?

Mathematics

1 answer:

spayn [35]4 years ago

5 0

Answer:

c)3/2(8/7)^x

Step-by-step explanation:

Evaluate the functions.

1. Because 7/4 > 1 and the exponent is positive,

the function does not decay.

2.Because 4/5 < 1 and the exponent is negative,

the function does not decay.

3. Because 8/7 > 1 and the exponent is negative,

the function decays.

4. Because 9/2 > 1 and the exponent is positive,

the function does not decay.

A composite plot the functions verifies the answer.

If all the x's are exponents, then 3/2 (8/7)^-x is the only one that decays as x gets bigger. That's because the base is greater than 1 and the x is negative.

please mark me brainliest :)

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Anyone can answer this

kolezko [41]

Answer:

y smaller than - 1/3

Step-by-step explanation:

.................

5 0

3 years ago

Y=x.arctan(x)^1/2. find dy/dx. pls show steps

Whitepunk [10]

$y=x(\arctan x)^{1/2}$

Use the product rule first:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dx}{\mathrm dx}(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

Use the chain rule to compute the derivative of $(\arctan x)^{1/2}$ . Let $z=(\arctan x)^{1/2}$ and take $u=\arctan x$ , so that by the chain rule

$\dfrac{\mathrm dz}{\mathrm dx}=\dfrac{\mathrm dz}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx}$

$\dfrac{\mathrm dz}{\mathrm du}=\dfrac{\mathrm du^{1/2}}{\mathrm du}=\dfrac12u^{-1/2}$

$\dfrac{\mathrm du}{\mathrm dx}=\dfrac{\mathrm d\arctan x}{\mathrm dx}=\dfrac1{1+x^2}$

$\implies\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}(1+x^2)}$

So we have

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+\dfrac x{2(\arctan x)^{1/2}(1+x^2)}$

You can rewrite this a bit by factoring $(\arctan x)^{-1/2}$ , just to make it look neater:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}}\left(2\arctan x+\dfrac x{1+x^2}\right)$

3 0

3 years ago

Convert 4 years to months

nikitadnepr [17]

Answer:

48 months

Step-by-step explanation:

12 times 4 48

3 0

3 years ago

Read 2 more answers

In △ABC AL is an angle bisector (L∈ BC ). Point M∈ AB so that LM=AM=BM. Find the angles in △ABC, if AC=2AL.

Diano4ka-milaya [45]

If AM=BM, then point M is a middle point of side AB.

1. Consider triangle AML. You know that AM=ML, then this triangle is isosceles and AL is its base. The angles adjacent to the base of isosceles triangle are conruent, this means that $\angle MAK\cong \angle AML.$

2. Consider lines ML and AC. The angle bisector AL is transversal. Since alternate interior angles $\angle MAK\cong \angle AML,$ you have that lines ML and AC are parallel. This means that ML is a middle line of triangle and 2ML=AC. Also you know that AC=2AL. This gives you that ML=AL. Now ML=AL and ML=AM gives you that triangle AML is equilateral.

3. In equilateral triangle AML all angles are congruent and have measures 60°. Thus, m∠AML=m∠MLA=m∠LAM=60°.

4. AL is angle bisector, then m∠MAL=m∠LAC=60° and m∠BAC=m∠MAL+m∠LAC=120°.

5. Consider ΔBML, it is isosceles, because BM=ML and m∠BML=180°-m∠AML=180°-60°=120°. Then,

$m\angle MBL=m\angle MLB=\dfrac{180^{\circ}-120^{\circ}}{2}=30^{\circ}.$

6. Consider triangle ABC. In this triangle m∠A=120°, m∠B=30°, then

m∠C=180°-m∠A-m∠B=180°-120°-30°=30°.

Answer: m∠A=120°, m∠B=m∠C=30°.

3 0

3 years ago

3000 per month for 40 years plus 5% equals how much money

Sveta_85 [38]

I hope you do not intend some sort of compounding.

Basically, 3000 per month for 40 years can be calculated by doing some simple maths. So 3000 x 12 to get for a complete year. Which is 36000. NOw we can multiply this value by 40 to get the correct amount. So that is 1440000.

Now five percent of this amount is 5 / 100 x 1440000 = 72000. So the final answer after adding 5 % would be 1512000.

8 0

3 years ago