Question

A local bakery opened with new equipment worth $80,000. Ten years later, the owners’ accountants told them that their equipment had depreciated at a rate of 6 percent per year. Which equation would you use to create a sequence modeling this situation?(1 point)
Responses

a n=80,000(0.94)^n

a n=80,000(0.06)^n

a n=80,000(0.94)^n−1

a n=80,000(0.06)^n−1

Answer 1

In a certain geographic location, a herd of elephants is declining at a rate of four percent every year. If there are currently 62 elephants in the herd, create an exponential decay function to model the problem. Let y represent the number of elephants after t years.(1 point)
Responses

y=62(1.04)^t

y=62(0.96)^t

y=62(0.04)^t

y=62(0.6)^t

Answer 2

To model the depreciation of the bakery's equipment, you want to use an equation that reflects a decrease in value due to the 6% annual depreciation rate. Since the equipment retains 94% of its value each year after depreciation, you can express this with the equation:

\[ a_n = 80,000(0.94)^n \]

This equation represents the value of the equipment \( a_n \) after \( n \) years, where it starts at $80,000 and decreases by multiplying by 0.94 for each year.

Therefore, the correct response is:

**a n=80,000(0.94)^n**

Answer 3

To model the exponential decay of the elephant population, you need to account for the decline at a rate of 4% per year. Since the herd is decreasing, you would use a factor representing the remaining population after the decline, which is 96% of the population each year (100% - 4% = 96%).

Thus, the correct exponential decay function for the number of elephants \( y \) after \( t \) years is:

\[ y = 62(0.96)^t \]

Therefore, the correct response is:

**y = 62(0.96)^t**