Answer:
The frog enclosure will reach maximum capacity after approximately 15 weeks.
Explanations:
The standard exponential equation is in the form;
Using the coordinate points (0, 100) and (1, 110) from the table, we can create a system of equation as shown:
Divide both equations to have:
Determine the value of a by substitute the value of b into any of the equation as shown:
Determine the equivalent exponential function
If the maximum capacity is 400 frogs, then f(x) = 400. On substituting into the resulting function, we will have:
Converting the expression into logarithm function
Determine the value of x
Hence the frog enclosure will reach maximum capacity after approximately 15 weeks.