Question

I need help please! I've been stuck on this for a week and its really stressful lol

Answer 1

Answer:

$y=0.2*4^{x}$

Step-by-step explanation:

Notice when x increases 1, y is 4 times the previous one, so

the function is like $y=C*4^{x}$

To determine the constant C, put any pair of (x, y)

Use x = 0, y = 0.2, so

0.2 = $C*4^{0}$ = C * 1 = C

then $y=0.2*4^{x}$

Answer 2

Answer:

$y=(0.2)4^x$

Step-by-step explanation:

General form of the exponential function: $y=ab^x$

Substituting the first point (0, 0.2) into the function:

$\implies 0.2=ab^0$

As any number to the zero power always gives one, $b^0=1$

$\implies0.2=a \times 1$

$\implies a=0.2$

Therefore, $y=(0.2)b^x$

Substituting the second point (1, 1.8) into the function:

$\implies0.8=(0.2)b^1$

$\implies0.8=(0.2)b$

$\implies b=\frac{0.8}{0.2}$

$\implies b=4$

So the final exponential equation is:

$y=(0.2)4^x$

Checking the equation with the remaining two points:

$x=2 \implies (0.2)4^2=3.2 \ \ \ \checkmark$

$x=3 \implies (0.2)4^3=12.8 \ \ \ \checkmark$