Question

The number of members for an e-commerce company was 1,700 in the year that the company started and has increased by 10% per year since then. Theexponential function of the number of members, M(f), in terms of t, the number of years since the year the company started, can be described by M(t) =1700(1.10). What is M(5) and its interpretation in the context of the problem?OM(5)-9350; After 5 years, there are approximately 9,350 members in the company.OM(5)=2737.867; After 5 years, there are approximately 2,737 members in the company.OM(5) 1786.717; After 5 years, there are approximately 1,786 members in the company.OM(5) 1870: After 5 years, there are approximately 1,8705 members in the company.W

Answer 1

Solution

Step 1

Given data

Initial members p = 1700

Rate of increase = 10% = 10/100 = 0.1

time t = 5

Step 2

Using exponential increase formula

$\begin{gathered} A\text{ = p\lparen1 + r\rparen}^t \\ \\ A\text{ = 1700}\times(1\text{ + 0.1\rparen}^5 \end{gathered}$

Step 3

Simplify the expression for the value of A

$\begin{gathered} A\text{ = 1700}\times1.1^5 \\ \\ A\text{ = 2737.867} \end{gathered}$

Final answer

After 5 years, there are approximately 2,737 members in the company.