According to information found on the production analysis page of the Inquirer, Digby sold 1129 units of Dome in the current year. Assuming that Dome maintains a constant market share, all the units of Dome are sold in the Nano market segment and the growth rate remains constant, how many years will it be before Dome will not be able to meet future demand unless the company adds production capacity? Exclude any existing inventory
To determine how many years it will be before Dome will not be able to meet future demand unless the company adds production capacity, we need to calculate the projected future demand for Dome in the Nano market segment based on the given information.
First, we need to find the growth rate of the Nano market segment. Unfortunately, the provided information does not include the growth rate. Therefore, it is not possible to calculate the exact number of years without this information.
However, if you have access to historic data on the growth rate in this market segment, you can use it to make an estimate. Let's say you find that the average annual growth rate of the Nano market segment is 5%. In that case, we can use this growth rate for estimation purposes.
To calculate the future demand, we can use the compound annual growth rate (CAGR) formula:
Future Demand = Current Demand * (1 + Growth Rate)^n
In this case, the current demand is given as 1129 units, the growth rate is assumed to be 5%, and we need to solve for "n," the number of years.
Let's plug the values into the formula and solve for "n":
Future Demand = 1129 * (1 + 0.05)^n
To find the value of "n," we need to take the logarithm of both sides of the equation. Assuming a base-10 logarithm:
log(Future Demand) = log(1129 * (1 + 0.05)^n)
Using logarithmic properties, we can simplify the equation:
log(Future Demand) = log(1129) + log(1 + 0.05)^n
Next, we isolate "n" by subtracting log(1129) from both sides:
log(1 + 0.05)^n = log(Future Demand) - log(1129)
Finally, divide both sides by log(1 + 0.05):
n = (log(Future Demand) - log(1129)) / log(1 + 0.05)
Using this formula and historical growth rate data, you can estimate the number of years it will be before Dome will not be able to meet future demand unless the company adds production capacity. Remember to replace the growth rate and future demand values with relevant data.