It's a basic algebra.. you dont need to know the meaning of 'r' or 'a'.
Let me try..
Q(13) ..
f(5) = 75.94 ===> t = 5
so, f(5) = Qo a^5 = Qo(1 + r)^5 = 75.94 -------- (i)
and, f(7) = 170.80 ===> t = 7 ;
so, f(7) = Qo a^7 = Qo (1 + r)^7 = 170.80 ------(ii)
Diving eq (ii) by equation (i);
Qo a^7 = 170.80 and Qo a^7 = Qo(1 + r)^7
------------ ---------- -------- --------------------- ------(iii)
Qo a^5 75.94 Qo a Qo (1 + r)^5
From left side equality,
a^2 = 2.249 ==> a = 1.5 ------- (iv)
From right equality of eqn (iii)
a^2 = (1 + r)^2
r = +- a - 1 ------ (v)
use 'a' from eqn (iv) in (v)
r = -2.5 and 0.5
I think 'r' can have +ve value only. So, r = 0.5
Try similarly for Question(14)
..:)