Respuesta :
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:
[tex]S.I = \frac{ prt}{100}[/tex]
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
[tex]p_0 = 1000[/tex]
[tex]r = 4 \% = \frac{4}{100} = 0.04[/tex]
Thus we can frame a function as:
total amount after "t" years = principal + simple interest
[tex]p(t) = p_0 + (p_0 \times r \times t )[/tex]
[tex]p(t) = 1000 + (1000 \times 0.04)t\\\\p(t) = 1000 + 40t[/tex]
Where, p(t) is the amount after "t" years and [tex]p_0[/tex] is the principal sum
Thus the function is obtained
