Write an exponential function in the form y = a b x y=ab x that goes through points ( 0 , 19 ) and (4,1539).

Respuesta :

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]