Discrete exponential growth and decay exercise answers

Here we give answers to several of the exercises on exponential growth and decay in discrete time.

Exercise 1

\begin{align*} {\rm{a.}} \hspace{2mm} x_t &= 1000 \times 1.2^t & x_{100} & = 1000 \times 1.2^{100} \approx 82,817,974,522 \\ {\rm{c.}} \hspace{2mm} B_t &= 138 \times 1.5^t & B_{100} & = 138 \times 1.5^{100} \approx 5.6 \times 10^{19} \\ {\rm{e.}} \hspace{2mm} P_t &= 1000 \times 1.2^t & P_{100} & = 1000 \times 1.2^{100} \approx 82,817,974,522 \\ {\rm{g.}} \hspace{2mm} c_t &= 1000 \times 0.9^t & c_{100} & = 1000 \times 0.9^{100} \approx 0.026 \end{align*}

Exercise 2

b. $x_4 = (1+r)^4 x_0$

c.\begin{align*} {\rm{(i.)}} \hspace{2mm} x_{t} & = 0.2^t \times 50 & x_{40} &\approx 73,489 \\ {\rm{(iii.)}} \hspace{2mm} x_{t} & = 1.05^{t} \times 50 & x_{40} &\approx 352 \end{align*}