Question

The number of visitors to a museum increases each year. The function

`V(t)=N(1+r)^{t}` represents the number of visitors to the museum at year t, where N is the number of visitors in year 0 and r is the rate of increase. Select the correct statement.

Answer 1

The function \( V(t) = N(1+r)^{t} \) describes the exponential growth of the number of visitors to a museum over time, where:

- \( V(t) \) is the number of visitors at year \( t \),
- \( N \) is the number of visitors in the base year (year 0),
- \( r \) is the rate of growth (expressed as a decimal), and
- \( t \) is the number of years since the base year.

Given this information, the correct statements about the function could be:

1. The number of visitors increases each year if \( r > 0 \).
2. The growth of visitors is exponential, meaning the number of visitors increases at an increasing rate as time goes on.
3. If \( r = 0 \), the number of visitors remains constant at \( N \).
4. As \( t \) increases, \( V(t) \) grows larger, highlighting a significant increase over time.

To select the correct statement, we would need to know which specific aspect you are asking about. Could you provide a specific list of statements or the context in which you want the correct statement?