Two retirement accounts grow according to the exponential models X(t)=300e^ 0.062t ,…
MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms
Problem
Two retirement accounts grow according to the exponential models
X(t)=300e0.062t,Y(t)=500e0.045t,
where t is measured in years since the initial deposits and the balances are in thousands of dollars.
(a) Determine, to the nearest tenth of a year, when the two account balances are equal.
(b) Calculate the common balance of the two accounts at that moment, to the nearest dollar.
(c) Find which account has the larger balance 25 years after the initial deposit and compute the difference between the two balances at that time.