Final answer:
The future value A is calculated using the formula A=Pe^rt with P=520, r=0.10, and t=0.75 years for the given time of 9 months. Substituting the values, we calculate A as 520 * e^(0.10 * 0.75).
Step-by-step explanation:
The student is asking how to calculate the future value A of a present value P after a certain time t with a continuous annual growth rate r. Given the formula A=Pe^rt where e is the base of the natural logarithm and is approximately 2.71828, P is the principal amount or present value which is 520, r is the annual growth rate which is 10% (or 0.10 as a decimal), and t is the time in years. As the time is given in months, it must be converted to years by dividing by 12. Therefore, for 9 months, t would be 9/12 or 0.75 years. Substituting the values into the formula, we calculate A as 520 * e^(0.10 * 0.75). The correct formula based on the information provided is: A=Pe^rt.