Bacteria quadruples on a daily basis. The population starts with 50 bacteria. Using the general exponential equation an = a1 • rn-1, what is the value of a1

Answer 1

In the general exponential growth equation \( a_n = a_1 \cdot r^{n-1} \):

• \( a_n \) is the population at time \( n \),
• \( a_1 \) is the initial population (the value we're looking for),
• \( r \) is the growth factor (the rate at which the population increases),
• \( n \) is the number of time intervals (days, in this case).

Given that the bacteria quadruple daily, the growth factor \( r \) is 4 (since quadrupling means multiplying by 4). The initial population of bacteria, denoted as \( a_1 \), is given in the problem as 50.

Thus, \( a_1 = 50 \).