Question

The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. The function below shows the relationship between f(x) and x:
f(x) = 10(1.3)x

Which of the following graphs best represents the function?

Graph of f of x equals 1.3 multiplied by 10 to the power of x
Graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinity
Graph of f of x equals 10 multiplied by 1.3 to the power of x
Graph of f of x equals 1.3 to the power of x

Answer 1

3rd one.

f(x) = 10(1.3)^x

Answer 2

Answer:

The  graphs that best represents the function is:

    Graph of f(x) equals 10 multiplied by 1.3 to the power of x.

Step-by-step explanation:

The function that shows the relationship between f(x) and x: is:

                    $f(x)=10\times (1.3)^x$

a)

Graph of f(x) equals 1.3 multiplied by 10 to the power of x.

This means that the expression is given by:

     $f(x)=1.3\times (10)^x$

Hence, option: a is incorrect since it is not equal to the given function f(x).

b)

Graph of exponential function going up from left to right in quadrant 1 through the point (0, 0) and continuing towards infinity.

In the given function f(x) when x=0 we have:

     $f(x)=10\times (1.3)^0\\\\\\f(x)=10\neq 0$

Hence, option: b is incorrect.

c)

Graph of f(x)  equals 10 multiplied by 1.3 to the power of x.

This means that the function f(x) is given by:

$f(x)=10\times (1.3)^x$

which is obviously true.

       Hence, option: c is correct.

d)

Graph of (x) equals 1.3 to the power of x.

This means that the function f(x) is given by:

$f(x)=(1.3)^x$

which does not m,atches the actual expression.

Hence, option: d is incorrect.