Question

1. since birth, harold has had a savings account that has been growing at a rate of 9% per year. the amount of money in the account can be modeled by the equation y = p(1.09)^x where y is the value of the account, and x is the number of years, and p was the original deposit amount. how much money is in the account if harold is 75 years old and the original deposit was $3000? answer: $ 10. calculate the area of the triangle if a = 11.6, b = 14, and c = 18.18. 81.2 79.77 77.46

Explanation:

Step1: Identify values for the compound - growth formula

We are given the formula $y = P(1.09)^{x}$, where $P = 3000$ (original deposit), and $x=75$ (number of years).

Step2: Substitute values into the formula

$y = 3000\times(1.09)^{75}$.
Using a calculator, first calculate $(1.09)^{75}$. Let $a=(1.09)^{75}\approx136.28349$.
Then $y = 3000\times a$.
$y=3000\times136.28349 = 408850.47$.

Step3: Solve for the area of the triangle

Since it's a right - triangle (as indicated by the right - angle symbol), the area formula for a right - triangle is $A=\frac{1}{2}ab$.
Here, $a = 11.6$ and $b = 14$.
$A=\frac{1}{2}\times11.6\times14$.
First, $\frac{1}{2}\times11.6 = 5.8$.
Then $5.8\times14=81.2$.

Answer:

For the first question: $\$408850.47$
For the second question: 81.2