Question

1. you invest $200 in an account. let t be the number of years since the investment was made. the value of the investment triples every 4 years. hint: need use ( y = a cdot b^t ). how much money is in the account after 12 years?

Explanation:

Step1: Identify initial value and growth factor

Initial investment $a = 200$, growth factor per 4 years is 3.

Step2: Calculate growth periods in 12 years

Number of 4-year periods: $\frac{12}{4} = 3$

Step3: Apply exponential growth formula

Use $y = a \cdot b^t$, where $b=3$, $t=3$.
$y = 200 \cdot 3^3$

Step4: Compute final value

$3^3 = 27$, so $y = 200 \times 27$

Answer:

5400