The exponential curve does look like a line when you zoom in very close to a point. For example, f(x) = e^x looks linear with slope e^x near x. You can see that

The exponential curve does look like a line when you zoom in very close to a point. For example, f(x) = e^x looks linear with slope e^x near x. You can see that, for small epsilon, e^(x+epsilon) - e^x is approximately epsilone^x, with an error term of the order of epsilon^2 e^x