Question

Use the following problem to answer questions 1-3.An investment can be modeled by the equation y = 12,000(.96)' where y is the amount of money in the investmentand t is the time in years,78,1.Is the investment increasing or decreasing?Answer:2.What was the initial investment?Answer:3. How much will the investment be worth in 10 years?Answer:

Answer 1

Question 1: Is the investment increasing or decreasing?

Answer: Decreasing

Reason: Checking the factor (0.96)^t the factor became lesser the higher the value of t.

Example: (0.96)^1 = 0.96, (0.96)^2 = 0.9216, (0.96)^3 = 0.884736

Question 2: What was the initial investment?

Answer: 12,000

Question 3: How much will the investment be worth in 10 years?

Solution:

$\text{ y = 12,000(0.96)}^t$$\text{ y = 12,000(0.96)}^{10}$$\text{ y = 12,000(}0.66483263599150104576)$$\text{ y = }7,977.99163189801254912\text{ }\approx\text{ 7,977.99}$

Answer: The investment will be worth 7,977.99 in 10 years.

Question 4: Find the annual sales in 7 years.

Equation:

$\text{ y = 650,000(1.04)}^t$

Solution:

$\text{ y = 650,000(1.04)}^7\text{ = }650,000(1.31593177923584)$$\text{ y = }855,355.656503296\text{ }\approx\text{ \ 855,355.66}$

Answer: After 7 years, considering the annual rate increase of 4%, the annual sales will be $855,355.66