Question

The first year Eleanor organized a fund-raising event,

she invited 30 people. For each of the next 5 years,
she invited double the number of people she had
invited the previous year. If f(n) is the number of
people invited to the fund-raiser n years after
Eleanor began organizing the event, which of the
following statements best describes the function f?

Answer 1

The function f(n) representing the number of people Eleanor invites to the fund-raiser after n years is an exponential function, given by f(n) = 30 × 2^n.

Step-by-step explanation:

The student's question relates to a scenario where Eleanor organizes a fund-raising event, inviting double the number of people each subsequent year compared to the previous one. We are provided with the initial value (30 people in the first year), and we are told that the number of people invited doubles each year. Therefore, we can describe the function f(n) which represents the number of people invited in year n as an exponential function with a base of 2.

f(n) = 30 × 2^n

This function takes the initial number (30) and raises 2 to the power of n, where n is the number of years after the first year.