Question

A quantity with an initial value of 980 grows exponentially at a rate of 9.5% every 7 years. What is the value of the quantity after 93 years, to the nearest hundredth?

Answer 1

To find the value of the quantity after 93 years, use the formula for exponential growth: Final Value = Initial Value * (1 + Growth Rate)^Number of Periods. Plug in the given values to find the answer.

Step-by-step explanation:

To find the value of the quantity after 93 years, we can use the formula for exponential growth:

Final Value = Initial Value * (1 + Growth Rate)^Number of Periods

Given that the initial value is 980, the growth rate is 9.5% or 0.095, and the number of periods is 93/7 = 13, we can plug these values into the formula:

Final Value = 980 * (1 + 0.095)^13.

Using a calculator, the value of the quantity after 93 years is approximately 2835.69.

Answer 2

To find the value of the quantity after 93 years, use the formula A = P(1 + r)ⁿ, where A is the final amount, P is the initial value, r is the growth rate as a decimal, and n is the number of time periods. Plugging in the given values, we find that the value is approximately 922.00 to the nearest hundredth.

Step-by-step explanation:

To find the value of the quantity after 93 years, we can use the formula for exponential growth: A = P(1 + r)ⁿ, where A is the final amount, P is the initial value, r is the growth rate as a decimal, and n is the number of time periods. In this case, P = 980, r = 0.095 (9.5% expressed as a decimal), and n = 93/7 = 13.2857 (rounded to 4 decimal places). Plugging in these values, we get:

A = 980(1 + 0.095)¹³.²⁸⁵⁷

Using a calculator or a spreadsheet, we can find that A ≈ 922.00 to the nearest hundredth.