Answer:
a) See below.
[tex]\textsf{b)} \quad y=940\left(1.0257\right)^{2x}[/tex]
c) x is the number of years.
d) y is the account balance in dollars.
e) $1728.29
Step-by-step explanation:
Part (a)
Interest is compounded semi-annually, so:
Therefore, calculate 1.0257% of the balance every 6 months:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \rm Years& \rm Account\;balance\;(\$) \\\cline{1-2} \vphantom{\dfrac12} 0& 940.00\\\cline{1-2} \vphantom{\dfrac12} 0.5& 964.16\\\cline{1-2} \vphantom{\dfrac12} 1& 988.94\\\cline{1-2} \vphantom{\dfrac12} 1.5&1014.35\\\cline{1-2} \vphantom{\dfrac12} 2&1040.42\\\cline{1-2} \vphantom{\dfrac12} 2.5&1067.16\\\cline{1-2} \vphantom{\dfrac12} 3&1094.59\\\cline{1-2} \end{array}[/tex]
Part (b)
An equation that models this situation is:
[tex]\implies y=940\left(1+\dfrac{0.0514}{2}\right)^{2x}[/tex]
[tex]\implies y=940\left(1.0257\right)^{2x}[/tex]
Part (c)
x is the number of years.
Part (d)
y is the account balance in dollars.
Part (e)
To calculate how much will be in the account after 12 years, substitute x = 12 into the equation from part (b):
[tex]\implies y=940\left(1.0257\right)^{2 \times 12}[/tex]
[tex]\implies y=940\left(1.0257\right)^{24}[/tex]
[tex]\implies y=940\left(1.8386054...\right)[/tex]
[tex]\implies y=1728.2890...[/tex]
Therefore, $1728.29 will be in the account after 12 years.
