Mathematics: Asap! which exponential function is represented by the table? a) f(x) = 0.2(0.5x) b) f(x) = 0.5(5x) c) f(x) = 0.5(0.2x) d) f(x) = 0.2(0.2x)

Where is the expression dude...

Asap! which exponential function is represented

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13.01.2022

Option C - f(x)=(0.5)(0.2)^x

Step-by-step explanation:

Given : The table of an exponential function.

To find : Which exponential function is represented by the table?

Solution :

First we create an exponential from the given table by taking any two values.

The general form of an exponential f(x)=ab^x

Now, putting values from the table,

x=-2 and f(x)=12.5

$12.5=ab^{-2}$ ....[1] '

x=-1 and f(x)=2.5

$2.5=ab^{-1}$ ....[2]

Now, dividing [1] and [2]

$\frac{12.5}{2.5}=\frac{ab^{-2}}{ab^{-1}}$

$5=b^{-1}$

$b=\frac{1}{5}$

b=0.2

Substitute in [2]

$2.5=a(0.2)^{-1}$

$a=2.5\times 0.2$

a=0.5

So, The exponential function with a=0.5 and b=0.2 is

f(x)=(0.5)(0.2)^x

Therefore, Option C is correct.

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