Answer:
[tex]y = 7(3^x)[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (0,7)[/tex]
[tex](x_2,y_2) = (4,567)[/tex]
Required
Determine the formula
An exponential function is of the form:
[tex]y = ab^x[/tex]
For point [tex](x_1,y_1) = (0,7)[/tex]
[tex]7 = ab^0[/tex]
[tex]7 = a*1[/tex]
[tex]7 = a[/tex]
[tex]a = 7[/tex]
For point [tex](x_2,y_2) = (4,567)[/tex]
[tex]567 = ab^4[/tex]
Substitute 7 for a
[tex]567 = 7*b^4[/tex]
Divide both sides by 7
[tex]81 = b^4[/tex]
Take 4th root of both sides
[tex]\sqrt[4]{81} =\sqrt[4]{b^4}[/tex]
[tex]\sqrt[4]{81} =b[/tex]
[tex]b = \sqrt[4]{81}[/tex]
[tex]b = 3[/tex]
Substitute 7 for a and 3 for b in [tex]y = ab^x[/tex]
[tex]y = 7 * 3^x[/tex]
[tex]y = 7(3^x)[/tex]
