Andrea invested $\$3,000$ in an online currency. If the value of the currency increases at a rate of 14\% per year, the situation can be modeled using the equation A(t) = 3,000(1.14)^t, where A is the amount in the investment after t years. What is the y-intercept

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

To find the y-intercept of the function modeled by the equation

\[ A(t) = 3,000(1.14)^t, \]

we need to evaluate the function at \( t = 0 \).

Substituting \( t = 0 \) into the equation:

\[ A(0) = 3,000(1.14)^0. \]

Since any number raised to the power of 0 equals 1:

\[ A(0) = 3,000 \cdot 1 = 3,000. \]

Thus, the y-intercept of the equation is \( 3,000 \).

Therefore, the answer is:

\[ \boxed{3000}. \]