Question

Please help me with this

Answer 1

Exponential Functions

Exponential functions are typically organized in this format:

$f(x) = a*c^x$

To find the equation given the graph of an exponential function:

1. Identify the horizontal asymptote
   ⇒ asymptote - a line towards which a graph appears to travel but never meets
   ⇒ If the horizontal asymptote is not equal to 0, we add this at the end of the function equation.
2. Identify the y-intercept
   ⇒ This is our a value.
3. Identify a point on the graph and solve for c

Solving the Question

Identify the horizontal asymptote

In this question, it appears to be x = 0.

Identify the y-intercept

The y-intercept is the value of y at which the graph appears to cross the y-axis. In this graph, it appears to be 100. This is our a value. Plug this into $f(x) = a*c^x$:

$f(x) = 100*c^x$

Solve for c

We can use any point that falls on the graph for this step. For instance, (1,50) appears to be a valid point. Plug this into our equation and solve for c:

$f(x) = 100*c^x\\50 = 100*c^1\\50 = 100*c\\\\c=\dfrac{1}{2}$

Plug c back into our original equation:

$f(x) = 100*(\dfrac{1}{2})^x$

Answer

$f(x) = 100*(\dfrac{1}{2})^x$