Joe starts a gym. In the first year, 300 people join. If the membership grows at an annual rate of 4%, how many members will there be after 5 years?
300*1.04^5
To find the number of members after 5 years, we need to calculate the membership growth for each year and add it to the previous year's total.
Step 1: Calculate the growth rate for each year
Since the membership grows at an annual rate of 4%, we need to calculate that growth for each year. To do this, we can use the formula:
Annual Growth = Previous Year's Total * (Growth Rate / 100)
Step 2: Calculate the number of members for each year
Starting with the initial membership of 300 people, we can calculate the number of members for each year:
Year 0 (Initial Year): 300 members
Year 1: Previous Year's Total + Annual Growth
Year 1 Total = 300 + (300 * (4 / 100))
Year 2: Previous Year's Total + Annual Growth
Year 2 Total = Year 1 Total + (Year 1 Total * (4 / 100))
Year 3: Previous Year's Total + Annual Growth
Year 3 Total = Year 2 Total + (Year 2 Total * (4 / 100))
Year 4: Previous Year's Total + Annual Growth
Year 4 Total = Year 3 Total + (Year 3 Total * (4 / 100))
Year 5: Previous Year's Total + Annual Growth
Year 5 Total = Year 4 Total + (Year 4 Total * (4 / 100))
Step 3: Calculate the final total after 5 years
The final total after 5 years will be the membership count at the end of Year 5.
Now, let's calculate the number of members for each year:
Year 0 (Initial Year): 300 members
Year 1: 300 + (300 * (4 / 100)) = 312 members
Year 2: 312 + (312 * (4 / 100)) = 324.48 (rounding to the nearest whole number) = 324 members
Year 3: 324 + (324 * (4 / 100)) = 336.96 (rounding to the nearest whole number) = 337 members
Year 4: 337 + (337 * (4 / 100)) = 349.48 (rounding to the nearest whole number) = 349 members
Year 5: 349 + (349 * (4 / 100)) = 361.96 (rounding to the nearest whole number) = 362 members
Therefore, there will be approximately 362 members after 5 years.