need help with exponential functions

[dusk cypress]

Problem:
Fuel prices have been increasing due to a 4% annual inflation rate. If the cost of a gallon of gasoline was $4.00 one year ago, what is it now?

Solution:
The cost of gasoline increases consistently by the same percentage each year, indicating an exponential pattern. If the price was $4.00 a year ago, it will have risen by 4% of $4.00, which is $0.16, resulting in a current price of $4.16.

To calculate the gasoline price after 5 years with this identical inflation rate, you can utilize the formula:
P = 4.16(1.04)^5

I am so frustrated that I still don't know how to translate problems to exponential functions. Initially, I thought the formula would be P = 4(1.04)^t but why the heck did they use 4.16. I think the starting value should be 4.00

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[crimson sedge]

This is because 4.00$ was last year

For this year you've calculated a price of 4.16$

For the years to come this is therefore the initial value