The graphs of two functions are shown. One is linear: $$y = 0.55x - 0.3$$ and the other is called exponential: $$f(x)=2^x + 0.025$$ Solving the equation $$2^x + 0.025 = 0.55x -0.3$$ would not be possible using our current algebra techniques. But in English, solving the equation means to find where the functions intersect. That we can do quite easily using graphs.

1. Find a value for $b$ such that the equation
   $$2^x + 0.025 = 0.55x + b$$
   has two solutions.
   If $b =$ then the equation would have two solutions.
2. Find a value for $b$ such that the equation
   $$2^x + 0.025= 0.55x + b$$
   has no solutions.
   If $b =$ then the equation would have no solutions.
3. Find a value for $b$ such that the equation
   $$2^x + 0.025= 0.55x + b$$
   has only one solution.
   If $b =$ then the equation would have only one solution.