Question

Tasha deposits money in a similar Certificate of Deposit account (CD). The balance in her account is described, with units as in Nick’s deposit, T(t)=650(1.03)tfor t ≥ 0. Use the structure of the expressions for N(t) and T(t) to describe how the two balances compare over time

Answer 1

The balance in Nick's account is described by the equation N(t) = 700(1.04)^t, while the balance in Tasha's account is described by T(t) = 650(1.03)^t.

From the equations, it can be seen that both balances increase over time as t increases, and both balances are multiplied by a constant factor for each unit of time that passes. However, the constant factor in Nick's equation (1.04) is greater than the constant factor in Tasha's equation (1.03), which means that Nick's balance is growing at a faster rate than Tasha's balance over time.

In other words, if the two accounts are given the same amount of time to grow, Nick's balance will be higher than Tasha's balance. This can be seen by comparing the values of N(t) and T(t) for different values of t.