Shown working but help appreciated! Complex algebra.
BACKGROUND INFORMATION: A researcher is interested in the buying behaviour (an indicator of demand) of a selected group of party pill users. In a controlled experiment, a new legalised party pill is put on to the market. Based on previous data, the researcher suggests the following demand model: D(t)=100−95(3/5)^t, t is measured in the number of weeks it has been on the market, and D(t) represents the percentage of the selected group wanting to buy the party pill after t weeks (D(t)=87, means 87% of the selected group).
After a short time though, the researcher has to revise his model because real data received from the outlet stores suggests that approximately 11 hours after the party pill went on the market, 50% of the selected group had purchased it. He revises his model to D(t)=100−95A^t. Find A and hence write the new model.
MY NEW MODEL: D(t)=100−95(0.00005529327)^t
MY QUESTION IS: Give a practical interpretation of the asymptotic behaviour for the function D(t) of your new model.
I know there is a trend. I just don't know what it is. Please help.