A store manager adjusts the price of an item each week that the item goes unsold. The price of the unsold item, in dollars, after x weeks can be modeled by the exponential function f(x) = 320(0.90)^x
The initial price of the store item before the store manager made any price adjustments was:
f(0) = 320(0.90)^0 = 320
To find the initial price of the store item before any price adjustments were made, you need to determine the price after 0 weeks.
The given exponential function to model the price is: f(x) = 320(0.90)^x
When x = 0, the formula becomes:
f(0) = 320(0.90)^0
Any number raised to the power of 0 is equal to 1. Therefore, (0.90)^0 = 1.
Substituting this back into the equation:
f(0) = 320(1)
320 multiplied by 1 is equal to 320.
Hence, the initial price of the store item before any price adjustments were made is $320.
The initial price of the store item before any adjustments were made can be found by plugging in x = 0 into the function f(x).
f(0) = 320(0.90)^0
Any number to the power of 0 is always 1, so the equation simplifies to:
f(0) = 320(1)
Therefore, the initial price of the store item before any adjustments were made is $320.