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Please help me with this

Please help me with this-example-1
User Akbor
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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=(1)/(2)

Plug c back into our original equation:


f(x) = 100*((1)/(2))^x

Answer


f(x) = 100*((1)/(2))^x

User Batalia
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