This formula says that the bank will TAKE three percent of the money
in your account whenever the account is inactive for a year. Nice bank !
Personally, I'd get ALL of my money out of that bank ASAP, and run,
don't walk, to a different bank.
Anyway, the equation is y = 7500(0.97)^x .
They want to know the y-intercept.
Just like the graph of ANY equation, the y-intercept is the place
where the graph is on the y-axis ... the place where x=0 .
What's the value of 'y' in this equation when x=0 ?
What's the value of (0.97)⁰ ?
Do you remember that ANY number raised to the zero power is ' 1 ' ?
(0.97)⁰ = 1
So, when x=0, y = 7500.
What does that mean ?
Well, the question tells you that 'y' is the value of an account "that was
left inactive for a period of 'x' years".
So x=0 at the beginning, when the money is first deposited, and
the account hasn't been inactive for ANY period yet.
When x=0, y=7500. The y-intercept is the amount of money that
the person originally deposited in the account. If he leaves the
account inactive, then the bank will multiply it by 0.97 each year ...
the same as reaching in and grabbing 3% of the money in the account !