To calculate the number of followers after eight years given the initial number of users and the yearly growth rate, we can use the formula for exponential growth:
\[ N = N_0 \cdot (1 + r)^t \]
Where:
- \( N \) is the number of followers at time \( t \).
- \( N_0 \) is the initial number of followers (500).
- \( r \) is the growth rate (0.778).
- \( t \) is the time in years (8).
Substituting the values into the formula:
\[ N = 500 \cdot (1 + 0.778)^8 \]
Calculating \( (1 + 0.778) \):
\[ 1 + 0.778 = 1.778 \]
Now raise it to the power of 8:
\[ 1.778^8 \approx 118.8393 \]
Now multiply by the initial number of followers:
\[ N \approx 500 \cdot 118.8393 \approx 59419.65 \]
Rounding to the nearest whole number, the expected number of followers after eight years is:
\[ N \approx 59420 \]
Thus, the statistician will have approximately 59,420 followers after eight years.