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 Tasha's Certificate of Deposit account grows at a rate of 3% per period, represented by the expression
`T(t)=650(1.03)^t,` where t is the time in periods. This is similar to Nick's deposit,
`N(t)=500(1.04)^t,`but with a different growth rate.

Step-by-step explanation:

In the given expressions,
`T(t)=650(1.03)^t` and
`N(t)=500(1.04)^t,` Tasha and Nick's Certificate of Deposit accounts are modeled as exponential functions of time (t), representing the balance at each time period. The structures of the expressions reveal that Tasha's account grows at a rate of 3% per period (1.03), while Nick's account grows at a rate of 4% per period (1.04).

The base of the exponent in each expression corresponds to the growth factor, determining how much the initial deposit increases over time. In Tasha's case, the growth factor is 1.03, indicating a 3% increase per period. This contrasts with Nick's 4% growth factor, showing a faster rate of growth.

Comparatively, Tasha's account experiences slower growth due to the lower growth rate, as represented by the 3% factor. Nick's account, with a 4% growth factor, accumulates at a faster pace over time. The structures of the expressions highlight the impact of the growth rate on the growth trajectory of the deposits.

In summary, Tasha's balance grows more slowly at a 3% rate, while Nick's balance grows faster at a 4% rate over time.

Answer 2

(1.06)0 = 1 and positive powers of 1.06 are larger than 1, thus the minimum value N(t) attains, if t≥0, is 400.

From the point of view of the context, a CD account grows in value over time so with a deposit of $400 the value will never drop to $399.