Question

1. the value of a savings account triples every year. after 3 years, half of the savings accounts value is $5,400. what was the value of the savings account at the start of the 3 years?

Explanation:

Step1: Find the value after 3 years

Let the value after 3 years be \( V \). We know that half of \( V \) is $5,400, so we can write the equation \(\frac{V}{2}=5400\). To find \( V \), we multiply both sides by 2: \( V = 5400\times2 = 10800 \).

Step2: Let the initial value be \( x \)

The value triples every year, so after 1 year it is \( 3x \), after 2 years it is \( 3\times(3x)=3^{2}x \), and after 3 years it is \( 3^{3}x \). We know that after 3 years the value is 10800, so \( 3^{3}x = 10800 \). Since \( 3^{3}=27 \), the equation becomes \( 27x = 10800 \).

Step3: Solve for \( x \)

To find \( x \), we divide both sides of the equation \( 27x = 10800 \) by 27: \( x=\frac{10800}{27}=400 \).

Answer:

The value of the savings account at the start of the 3 years was $400.