Question 11 Suppose a long term investment is modeled by the exponential function \( V(t)=30(25)^{\frac{1}{20}} \) where \( V(t) \) is the total value after \( t \) year. What does 25 represent in the equation? the growth factor the number of years the interest rate thitial deposit

To understand what the number 25 represents in the exponential function \( V(t) = 30(25)^{\frac{1}{20}} \), let's analyze the components of the equation. 1. **Exponential Function Structure**: The general form of an exponential growth function is \( V(t) = P \cdot (1 + r)^t \), where: - \( P \) is the initial amount (or principal), - \( r \) is the growth rate (interest rate), - \( t \) is the time in years. 2. **Identifying Components**: - In the given function, \( 30 \) is the initial deposit (or principal). - The term \( (25)^{\frac{1}{20}} \) indicates a growth factor, as it is raised to a power that relates to time. 3. **Understanding the Number 25**: - The base of the exponent (25) typically represents the growth factor in an exponential function. It indicates how much the investment grows over a specific period. - The exponent \( \frac{1}{20} \) suggests that this growth factor is being applied over a time frame of 20 years. Based on this analysis, the number 25 represents the **growth factor** in the equation. Thus, the correct answer is: - **the growth factor**.