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galben [10]
3 years ago
14

What function represents the pattern shown in the table?

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
7 0

Given:

The table of values of an exponential function.

To find:

The function for the given table of values.

Solution:

The general exponential function is:

y=ab^x        ...(i)

Where, a is the initial value and b is growth factor.

From the given table it is clear that the function passes through the points (1,9) and (2,36). It means the function must be true for these two points.

9=ab^1        ...(ii)

36=ab^2       ...(iii)

On dividing (iii) by (ii), we get

\dfrac{36}{9}=\dfrac{ab^2}{ab}  

4=b  

Putting b=4 in (ii), we get

9=a(4)^1

\dfrac{9}{4}=a

Putting a=\dfrac{9}{4},b=4 in (i), we get

y=\dfrac{9}{4}(4)^x

y=9(4)^{x-1}

The function notation with variable n is:

f(n)=9(4)^{n-1}

Therefore, the correct option is D.

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3 years ago
Determine if the equation y = 2(0.45)x represents exponential growth or decay
djverab [1.8K]
We have that
y = 2(0.45)^x

in this problem 
2-----------> is the Coefficient
0.45-------> is the Base
<span>x-----------> is the Exponent

we know that
</span><span>If the base  is less than 1 (but always greater than 0), the function will be exponential decay
</span>It is decay because as x values increase, y values decrease.
<span>0.45 < 1  and 0.45 > 0
therefore

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</span>y = 2(0.45)^x
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the answer is
exponential decay<span>

</span>
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3 years ago
The following data table represents the total cost of a monthly cell phone bill as a function of the number of minutes that the
Alisiya [41]
Answer:
The total monthly cost would be $214

explanation:
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