Question

Brainliest + points!!!

Answer 1

Answer: $y = 5.88(1.24)^x$

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:

$y = a(b)^x$

Let us take first point and plug in above exponential equation, we get

$5 = a(b)^{-3}$

On applying negative exponents rule $a^{-n}= 1/a^n$, we get

$5 = \frac{a}{b^3}$

On cross multiplying, we get

$5b^3 =a.$  ------------(1).

Now, plugging (1,12) in above exponential equation, we get

$12 = a(b)^{1}$  

$12 = ab$     --------------(2).

Substituting $a=5b^3$ in second equation, we get

$12 = (5b^3)\times b$

$12 = 5b^4$

Dividing both sides by 5, we get

$\frac{12}{5} =\frac{5b^4}{5}$

$2.4=b^4$

Taking 4th root on both sides, we get

$b =\sqrt[4]{2.4}$

b= 1.24.

Plugging b = 1.24 in first equation, we get

$a = 5(1.24)^3$

a=5.88.

Plugging values of a and b in $y = a(b)^x$, we get

$y = 5.88(1.24)^x$