Answer:
The function is [tex]y=19(3)^x[/tex]
Explanation:
Given: An exponential function in the form [tex]y=ab^x[/tex] goes through points ( 0 , 19 ) and (4,1539)
To find: the function
Solution:
Put [tex](x,y)=(0,19)[/tex] in [tex]y=ab^x[/tex]
[tex]19=ab^0=a(1)=a[/tex]
So, [tex]y=19b^x[/tex]
Put [tex](x,y)=(4,1539)[/tex] in [tex]y=ab^x[/tex]
[tex]1539=19b^4\\\frac{1539}{19}=b^4\\81=b^4\\3^4=b^4\\3=b[/tex]
So, [tex]a=19,b=3[/tex]
The function is [tex]y=19(3)^x[/tex]