The function the represent the balance in the account as a function of time t is p(t) = 1000 + 40t
<h3><u>Solution:</u></h3>
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}](https://tex.z-dn.net/?f=S.I%20%3D%20%5Cfrac%7B%20prt%7D%7B100%7D)
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](https://tex.z-dn.net/?f=p_0%20%3D%201000)
![r = 4 \% = \frac{4}{100} = 0.04](https://tex.z-dn.net/?f=r%20%3D%204%20%5C%25%20%3D%20%5Cfrac%7B4%7D%7B100%7D%20%3D%200.04)
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 )](https://tex.z-dn.net/?f=p%28t%29%20%3D%20p_0%20%2B%20%28p_0%20%5Ctimes%20r%20%5Ctimes%20t%20%29)
![p(t) = 1000 + (1000 \times 0.04)t\\\\p(t) = 1000 + 40t](https://tex.z-dn.net/?f=p%28t%29%20%3D%201000%20%2B%20%281000%20%5Ctimes%200.04%29t%5C%5C%5C%5Cp%28t%29%20%3D%201000%20%2B%2040t)
Where, p(t) is the amount after "t" years and
is the principal sum
Thus the function is obtained