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Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 3)(0,3) and (4, 7203)(4,7203).

Sagot :

MrRoyal

Answer:

[tex]y = 3(7)^x[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (0,3)[/tex]

[tex](x_2,y_2) = (4,7203)[/tex]

Required

Determine an exponential function

Substitute 0 for x and 3 for y in [tex]y=ab^x[/tex]

[tex]3 = ab^0[/tex]

[tex]3 = a*1[/tex]

[tex]3 = a[/tex]

[tex]a = 3[/tex]

Substitute 4 for x and 7203 for y in [tex]y=ab^x[/tex]

[tex]7203= ab^4[/tex]

Substitute 3 for a

[tex]7203= 3*b^4[/tex]

Divide both sides by 3

[tex]2401= b^4[/tex]

Take 4th root of both sides

[tex]\sqrt[4]{2401} = b[/tex]

[tex]7 = b[/tex]

[tex]b = 7[/tex]

Substitute 3 for a and 7 for b in [tex]y=ab^x[/tex]

[tex]y = 3(7)^x[/tex]

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