Pam owns an electronics store with storage capacity for 100 computer tablets. She currently has 90 computer tablets in inventory and determines that they are selling at a daily rate equal to 17% of the available capacity. When will Pam sell out of computer tablets?
To determine when Pam will sell out of computer tablets, we need to calculate how many tablets she is selling per day and then divide the number of tablets she has in inventory by the daily sales rate.
First, let's calculate the daily sales rate:
Daily sales rate = Available capacity * Sales rate
Sales rate = 17% = 0.17 (in decimal form)
Available capacity = 100 tablets
Daily sales rate = 100 * 0.17 = 17 tablets per day
Now, let's calculate how many days it will take for Pam to sell out of computer tablets:
Days to sell out = Inventory / Daily sales rate
Inventory = 90 tablets
Days to sell out = 90 / 17 ≈ 5.29
Since we can't have fractional days, we need to round up to the nearest whole number. Therefore, it will take Pam approximately 6 days to sell out of all the computer tablets in her inventory.
To determine when Pam will sell out of computer tablets, we can start by finding the daily sales rate.
Step 1: Calculate the daily sales rate:
Available capacity = 100 computer tablets
Daily sales rate = 17% of 100 computer tablets
Daily sales rate = 17/100 * 100
Daily sales rate = 17 computer tablets
Step 2: Calculate the number of days it will take to sell out of computer tablets:
Number of tablets in inventory = 90 computer tablets
Number of days to sell out = Number of tablets in inventory / Daily sales rate
Number of days to sell out = 90 / 17
Number of days to sell out ≈ 5.29
Therefore, Pam will sell out of computer tablets in approximately 5.29 days.
the available capacity with an inventory of y is 100-y
so, we have
dy/dt = -0.17(100-y)
That is, putting it into the usual LDE form,
y' + 0.17y = -17
y = 100-c*e^(.17x)
Now use y(0) = 90 to find c and when y=100