Question

Write a function to represent each problem situation Carmen deposits $1000into simple interest account.The rate for the account is 4%.Write a function the represent the balance in the account as a function of time t

Answer 1

The function the represent the balance in the account as a function of time t is p(t) = 1000 + 40t

Solution:

Given that,

Carmen deposits $1000 into simple interest account

The rate for the account is 4%

To find: function the represent the balance in the account as a function of time t

Given is simple interest account

The formula for simple interest is given as:

$S.I = \frac{ prt}{100}$

Where, "p" is the principal and "r" is the rate of interest and "t" is the number of years

In simple interest,

total amount after "t" years = principal + simple interest

Here in this question, Carmen deposits $1000

$p_0 = 1000$

$r = 4 \% = \frac{4}{100} = 0.04$

Thus we can frame a function as:

total amount after "t" years = principal + simple interest

$p(t) = p_0 + (p_0 \times r \times t )$

$p(t) = 1000 + (1000 \times 0.04)t\\\\p(t) = 1000 + 40t$

Where, p(t) is the amount after "t" years and $p_0$ is the principal sum

Thus the function is obtained