3. During an economic recession, a firm decides to decrease its output, y, at a constant relative rate over a certain number of years. At t = 0, the firm’s current output level is 2000 units. Two years later, it is 500 units.(a) Find a formula for the size of the output, y(t).(Hint: Use (ln( 1/4))/2 = -0.6931) (b) Find the annual percent rate of decrease in the firm’s output to achievethis target.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
3. During an economic recession, a firm decides to decrease its output, y, at a constant relative rate over a certain number of years. At t = 0, the firm’s current output level is 2000 units. Two years later, it is 500 units.
(a) Find a formula for the size of the output, y(t).
(Hint: Use (ln( 1/4))/2 = -0.6931)
(b) Find the annual percent rate of decrease in the firm’s output to achieve
this target.
Let the annual percent rate of decrease in the firm’s output to achieve this target be r.
Part (a)
Hence, the formula for the size of the output, y(t) will be:
y(t) = y0(1 - r)t where t is in years and y0 is the firm's current output level at t = 0.
y0 = 2,000
Hence, the desired formula:
y(t) = 2,000(1 - r)t
Step by step
Solved in 4 steps
