Question

Which exponential function is represented by the values in the table?

Answer 1

Answer:

$\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x$

Step-by-step explanation:

Exponential Function

The exponential function can be written with the general equation:

$f(x)=A\cdot r^x$

Where A is the value when x=0 and r>0 is the ratio. If r is greater than 1, the function is increasing, if r is less than 1, the function is decreasing.

The table shows the relation between values of x and values of the function y. Note that as x increases (one by one), y decreases with a ratio of 1/2. Only the last two choices have ratios of r=1/2. We only have to test which one of them has the correct value of y=4 when x=0.

Substituting in the third function:

$\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x$

$\displaystyle f(0)=4\cdot\left(\frac{1}{2}\right)^0$

$f(0) = 4$

This gives the correct value of f(0)=4.

Substituting in the fourth function:

$\displaystyle f(x)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^x$

$\displaystyle f(0)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^0$

$f(0) = \frac{1}{2}$

This choice is wrong

Correct choice:

$\boxed{\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x}$