Question

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 x-intercept

Answer 1

To find the x-intercept of the function \( A(t) = 3000(1.14)^t \), we need to determine when the amount in the investment, \( A(t) \), equals zero. The x-intercept occurs when the function \( A(t) \) is equal to zero:

\[
3000(1.14)^t = 0
\]

In this equation, \( 3000(1.14)^t \) cannot equal zero for any real value of \( t \) because \( 1.14^t \) (an exponential function) is always positive for all real numbers \( t \), and multiplying a positive number (like \( 3000 \)) by a positive number can never result in zero.

Thus, there is no value of \( t \) that can satisfy the equation \( 3000(1.14)^t = 0 \).

Therefore, the x-intercept does not exist.