Answer:
[tex]y=(750)1.05^t[/tex], where [tex]t[/tex] is the time (in years) from investment
Or [tex]y=(750)1.05^{t-5}[/tex], where [tex]t[/tex] is the age of James
Step-by-step explanation:
exponential model: [tex]y=ab^t[/tex], where [tex]t[/tex] is the time (in years) from investment
when t = 0, y = 750
[tex]\implies 750=ab^0[/tex]
As [tex]b^0=1[/tex]
[tex]\implies 750=a[/tex]
Therefore, [tex]y=750b^t[/tex]
If the savings increase by 5% each year, then b = 105%.
105% = 105/100 = 1.05
Therefore, b = 1.05
So final model: [tex]y=(750)1.05^t[/tex], where [tex]t[/tex] is the time (in years) from investment
Or, we can write this as [tex]y=(750)1.05^{t-5}[/tex], where [tex]t[/tex] is the age of James
