Estimate the slope of … at

This problem is about exponential $v$’s and $f$’s.

Estimate the slope of $f(t)=2^t$ at $t=0$. Use a calculator to compute (increase in $f$)/(increase in $t$) when $t$ is small:
$$\frac{f(t)-f(0)}{t}=\frac{2^{-1}-1}{1}\text{ and }\frac{2^{.1}-1}{.1}\text{ and }\frac{2^{.01}-1}{.01}\text{ and }\frac{2^{.001}-1}{.001}.$$

Its source prints no answer for this problem, so there's nothing to check against.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §1.2 Calculus Without Limits, #37