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)

Answer 1

To model the depreciation of the bakery's equipment, we can use an exponential decay formula. The general formula for depreciation can be expressed as:

\[ V(t) = V_0 \times (1 - r)^t \]

Where:
- \( V(t) \) is the value of the equipment after \( t \) years,
- \( V_0 \) is the initial value of the equipment ($80,000 in this case),
- \( r \) is the depreciation rate (6% or 0.06), and
- \( t \) is the number of years.

Substituting in the values for this specific case, we get:

\[ V(t) = 80000 \times (1 - 0.06)^t \]

This simplifies to:

\[ V(t) = 80000 \times (0.94)^t \]

Thus, the equation you would use to create a sequence modeling this situation is:

\[ V(t) = 80000 \times (0.94)^t \]

Where \( t \) represents the number of years since the bakery opened.