Final answer:
A logarithmic curve begins with a rapid increase which then slows down and levels off, making it the correct answer for a curve that starts off big and tapers off toward the end.
Step-by-step explanation:
The type of curve that starts off big in the beginning and then tapers off toward the end is known as a logarithmic curve. This type of curve has a rapid increase at the beginning, which quickly slows down and approaches a horizontal asymptote, meaning it levels off as it progresses along the x-axis. In contrast, an exponential curve would be characterized by a slow start with growth that accelerates over time.
A linear curve has a consistent rate of increase or decrease, and a quadratic curve takes on the shape of a parabola with either a concave up or down orientation depending on the leading coefficient.