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bogdanovich [222]
3 years ago
9

Determine weather each table represents a linear, quadratic, or exponential function.

Mathematics
1 answer:
solong [7]3 years ago
3 0

Answer:

A: Exponential

B: Quadratic

C: Linear

Step-by-step explanation:

Solution:-

- We will closely inspect each Table and find the difference between each "Y" value at every unit increase in "x" value:

Table A:

 X            Y              ΔY/ΔX

 1             5               xxxxxx              Exponential because [ ΔY/ΔX ]          

 2            11              11 - 5 = 6            increases at the fastest rate out of all

 3           29             29 - 11 = 18         functions.

 4           83             83 - 29 = 54

 5           245          254 - 83 = 171

 6           731           731 - 254 = 477

Table B:

 X            Y                 ΔY/ΔX            Δ^2Y/ΔX^2          

 0             5                 xxxxxx              xxx             Quadratic because

 1              7                 7 - 5 = 2            xxx            Δ^2Y/ΔX^2 is a constant

 2             13               13 - 7 = 6           6-2 = 4       for all quadratic functions

 3             23              23 - 13 = 10       10-6 = 4

 4             37              37 - 23 = 14       14-10 = 4

 5             55             55 - 37 = 18        18-14 = 4

Table C:

 X            Y                 ΔY/ΔX                      

 3             20               xxxxxx                 Linear because

 6             18                 2 / 3                    ΔY/ΔX is a constant

 9             16                 2 / 3                   for all linear functions

 15            12                 2 / 3      

 27            4                  8/12 = 2/3      

 39           -4                  8/12 = 2/3      

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Step-by-step explanation:

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Let f(x) = cx^k be a power function such that f(13) is four times the size of f(1). What is the power k?
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Answer:

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Step-by-step explanation:

Hi there,

To get started in order to solve this, please recall the property of logarithms.

This question is a bit tricky, but doable. Best way to solve this is first compare the two functions:

f(x) = cx^{k} \\ f(13)=4f(1)  

Now, let's see what the function gives at 13 and 1:

f(13)=c13^{k}\\f(1)=c1^{k}

Something to recognize is that 1 to the power of <em>anything</em> is just 1, so f(1) is reduced to:

f(1)=c  We are making progress!

Next, we can set both f(13) forms equivalent to each other, watch this:

f(13)=f(13) = 4f(1) but we know what f(1) is equal to, and let's substitute our knowns:

c13^{k}=4c1^{k} = 4c the c constant on both left and right side cancel out:

13^{k}=4 Now, take the logarithm form of both side of the equation. I used natural log, but you can also use common logs:

ln(13^{k})=ln(4)  ⇒ k*ln(13)=ln(4) this was performed using <em>the power  log rule. </em>

Isolate k:

k=\frac{ln(4)}{ln(13)} =0.540 using a calculator.

If you liked this solution, hit Thanks or give a rating!

thanks,

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