- Both functions have variables.
- Both functions have inputs.
- Both functions have outputs.
- The graph of a linear functions produces a straight line, and the graph of an exponential function produces a curve.
- The graph of an exponential function has an asymptote, while the graph of a linear function doesn't.
- The basic exponential function has a y-int at (0,1)
- Linear functions have no exponents.
2) The y-int is 3 and the growth factor is 4.
4) a is less than 1, because the graph shows an exponential decay.
5) f(x)=2 (5^x)
There are 24 hours in a day. We came up with the equation f(x)=2^(t/6) because the questions states that the bacteria doubles every 6 hours... therefore the growth factor is 2, and t/6 is the exponent. The question also states that the equation we came up with is equivalent to a sixteen fold increase, so we also let that equal f(x). We plugged in the values, and found that they equal each other.