To calculate the number of members the gym will have in 5 years with a 9.4% annual increase, we can use the formula for compound interest, which can also be applied to this situation:
\[ A = P(1 + r)^t \]
Where:
- \( A \) is the amount of members after \( t \) years,
- \( P \) is the initial number of members,
- \( r \) is the annual growth rate (as a decimal),
- \( t \) is the number of years.
Given:
- \( P = 143 \)
- \( r = 9.4% = 0.094 \)
- \( t = 5 \)
Now we can plug in the values:
\[ A = 143(1 + 0.094)^5 \]
Calculating \( (1 + 0.094)^5 \):
\[ (1.094)^5 \approx 1.5154 \]
Now multiply this by the initial number of members:
\[ A \approx 143 \times 1.5154 \approx 216.2022 \]
Rounding to the nearest whole number, the gym will have approximately:
\[ \boxed{216} \]
members in 5 years.