#### Answer

a. $ 1\%$
b. 69 years

#### Work Step by Step

Exponential growth model: $A=A_{0}e^{kt} \qquad(k>0)$
($A_{0}$ is the initial quantity, $A$ is the quantity after time t).
-----------
a.
Reading k directly from the model $A=4.3e^{0.01t},$
$k=0.01$,
( New Zealand's growth rate is $ 1\%$)
$\mathrm{b}$.
Using the given formula for doubling time,
$ t=\displaystyle \frac{\ln 2}{0.01}\approx$69.314718056
To the nearest whole year:
69 years.