An exponential model has a starting amount times a base raised to the number of time intervals. The base is the factor applied whenever the exponent goes up by , so read the time unit before interpreting it. Don't confuse multiplying the current value with adding a fixed amount.
Hints
- Hint 1
The initial value is the value at . Since counts years since 2005, what year is ? Remember that a nonzero number raised to the power equals .
- Hint 2
Compare the model at with the model at . That one-year step adds one more copy of the base to the product. How does the new value relate to the previous value?
Step-by-step
Read the exponential model
Step 1Identify the starting value
No Desmos needed. The model shows the yearly factor directly. Since counts years since 2005, substitute to find the value in 2005:
Any nonzero number raised to the power equals , so:
The starting value is $12,500, not .
- Step 2
Find what happens each year
Each one-year step increases by . Substitute into the model:
Use to pull out one more factor:
Recognize that is :
So the growth factor multiplies the previous year's value. Because , the collection grows rather than decreases. The value of the collection is multiplied by each year. Choice D.