Question

The number of members over time in an online music sharing club can be modeled by an exponential function. the club started with 2100 members. After 1 month, the club had 2142 members.
a. Write an equation for the number of members as a function of time in months since the club started.
b. What is the parameter b in the equation, and what does it represent in this situation?
c. Will the club have more than 5000 members during its first year? Justify your reasoning.

Answer 1

Answer:

a.) $N(x) = N_{0} e^{bx}$

b.) therefore b = $\ln \frac{2142}{2100} = \ln (1.02) = 0.0198$

    b is the rate of increase of number of members

c.) The club will not be able to get more than 5000 members during its first year.

Step-by-step explanation:

i) the club started with 2100 members.

  so we can write $N_{0}$ = 2100.

a.) so we can write the equation as an exponential function given by

  $N(x) = N_{0} e^{bx}$ where x is in months and b is a constant and N(x) is the number of members in the online music sharing club .

 therefore 2142 = 2100 $\times (e^{b\times 1})$ = 2100$e^{b}$

b.) therefore b = $\ln \frac{2142}{2100} = \ln (1.02) = 0.0198$

    b is the rate of increase of number of members

c.) Will the club have more than 5000 members during its first year? Justify your reasoning.

      5000 = 2100$e^{0.0198x}$

 therefore x  = $\frac{1}{0.0198} \ln{(\frac{5000}{2100} )} = 43.81 \hspace{0.1cm}months$

The club will not be able to get more than 5000 members during its first year.