Answer
a. r is very close to 1, the model fits the data well.
b. by $ 1\%$
Work Step by Step
$\mathrm{a}$.
(I used desmos.com, an online calculator. See image below)
The exponential model is
$y=202.4(1.01)^{x}$
Since $r\approx 0.999$ is very close to 1,
the model fits the data well.
$\mathrm{b}$.
Use Basic Logarithmic Properties: $b^{\log_{b}x}=x$,
replacing b with e and x with $(1.01)^{x}$
$y=202.4(1.01)^{x}$
$y=202.4e^{(\ln 1.01)x}$
$y=202.4e^{0.00995x}$
Since $k=0.00995 \approx 1\%$
the USA population is increasing by about $ 1\%$ each year.
