Question

Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 20)(0,20) and (2, 720)(2,720).

Answer 1

Answer:

The exponential function that goes through $(x_{1},y_{1}) = (0,20)$ and $(x_{2}, y_{2}) = (2,720)$ is $y = 20\cdot 6^{x}$.

Step-by-step explanation:

Let be an exponential function of the form $y = a\cdot b^{x}$ that goes through $(x_{1},y_{1}) = (0,20)$ and $(x_{2}, y_{2}) = (2,720)$. Then, we have the following system of equations:

$20 = a\cdot b^{0}$ (1)

$720 = a\cdot b^{2}$ (2)

By dividing (2) by (1), we obtain the value for $b$:

$\frac{720}{20} = b^{2}$

$b = \sqrt{\frac{720}{20} }$

$b = 6$

And the value for $a$ is found by (1):

$a = 20$

The exponential function that goes through $(x_{1},y_{1}) = (0,20)$ and $(x_{2}, y_{2}) = (2,720)$ is $y = 20\cdot 6^{x}$.