Respuesta :
Answer: [tex]y = 5.88(1.24)^x[/tex]
Step-by-step explanation: We are given points (−3,5),(1,12),(5,72),(7,137).
We know the equation of an exponential modal is:
[tex]y = a(b)^x[/tex]
Let us take first point and plug in above exponential equation, we get
[tex]5 = a(b)^{-3}[/tex]
On applying negative exponents rule [tex]a^{-n}= 1/a^n[/tex], we get
[tex]5 = \frac{a}{b^3}[/tex]
On cross multiplying, we get
[tex]5b^3 =a.[/tex] ------------(1).
Now, plugging (1,12) in above exponential equation, we get
[tex]12 = a(b)^{1}[/tex]
[tex]12 = ab[/tex] --------------(2).
Substituting [tex]a=5b^3[/tex] in second equation, we get
[tex]12 = (5b^3)\times b[/tex]
[tex]12 = 5b^4[/tex]
Dividing both sides by 5, we get
[tex]\frac{12}{5} =\frac{5b^4}{5}[/tex]
[tex]2.4=b^4[/tex]
Taking 4th root on both sides, we get
[tex]b =\sqrt[4]{2.4}[/tex]
b= 1.24.
Plugging b = 1.24 in first equation, we get
[tex]a = 5(1.24)^3[/tex]
a=5.88.
Plugging values of a and b in [tex]y = a(b)^x[/tex], we get
[tex]y = 5.88(1.24)^x[/tex]
