Final answer:
To find the amount of money in an account over time, an exponential growth equation is typically used when the growth rate is consistent, represented as A = Pe^rt. This is the correct option (A) for the final answer.
Step-by-step explanation:
To find an equation that gives the amount of money in an account after t years, we must identify the type of growth the account experiences. If the account grows by a constant rate relative to its current amount, this is characterized as exponential growth.
This growth can be represented by the equation A = Pert, where A is the amount of money after t years, P is the principal amount, r is the annual growth rate, and e is the base of the natural logarithm.
For a linear growth, represented by a straight line, the equation would be A = mt + b, where m is the slope or the rate of increase, and b is the starting amount.
A logarithmic function might be used in cases of diminishing returns over time, represented by A = a + b log(c), where a, b, and c are constants and c is greater than 1.
Lastly, a quadratic function represents a parabolic growth, such as A = at2 + bt + c.
Given the information provided, which suggests a consistent rate of growth, the correct option for the final answer is A) Exponential Growth.