he amount M (in billion of dollars) of mortgage debt outstanding in the US from 1990 to 2001 can be approximated by the function
M(t)= 29.9t^2 + 3892 where t=0 represents 1990.
Rewrite the function so that t=0 represents 2000.
2000 = 1990 + 10
M ( t ) = 29.9 ( t + 10 ) ^ 2 + 3892
M ( t ) = 29.9 ( t ^ 2 + 2 t * 10 + 10 ^ 2 ) + 3892
M ( t ) = 29.9 ( t ^ 2 + 20 t + 100 ) + 3892
M ( t ) = 29.9 t ^ 2 + 29.9 * 20 t + 29.9 * 100 + 3892
M ( t ) = 29.9 t ^ 2 + 598 t + 2990 + 3892
M ( t ) = 29.9 t ^ 2 + 598 t + 6882
To rewrite the function so that t=0 represents 2000 instead of 1990, we need to shift the variable t by 10 years.
In the original function, t=0 represents 1990. This means that when t=0, it corresponds to the year 1990.
To represent 2000 as t=0, we need to shift t by 10 years. This means that when t=10, it corresponds to the year 2000.
So, we can rewrite the function as:
M(t) = 29.9(t-10)^2 + 3892
Now, when t=10, it corresponds to the year 2000.