Question

Write an exponential function to model the situation, then find the amount after the specified time.

A population of 1,860,000 decreases 1.5% each year for 12 years.
A) y = 1,860,000(1.05)^12; 3,340,293
B) y = 1,860,000(1.05)^(-12); 1,035,718
C) y = 1,860,000(0.985)^12; 1,551,485
D) y = 1,860,000(0.95)^12; 1,005,070

Answer 1

To model the situation, we use the formula y = A(1 - r)^t, where A is the initial amount, r is the rate of decrease, and t is the time in years. Plugging in the values, we find that the correct answer is C) y = 1,860,000(0.985)^12; 1,551,485.

Step-by-step explanation:

To model the situation, we can use the formula y = A(1 - r)^t, where A is the initial amount, r is the rate of decrease as a decimal, and t is the time in years. In this case, the initial population is 1,860,000 and the rate of decrease is 1.5%, or 0.015. So the exponential function to model the situation is y = 1,860,000(1 - 0.015)^12.

Simplifying this equation, we get y = 1,860,000(0.985)^12.

Now, we can find the amount after 12 years by plugging in the value of t into the equation. Evaluating the equation, we get y = 1,860,000 * 0.8135 = 1,511,029.5.

Therefore, the correct answer is C) y = 1,860,000(0.985)^12; 1,551,485.