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

Question

asked Nov 4, 2023 121k views

2 Answers

Diceyus · Answer 1 · 2023-11-07T17:16:52+0000

Answer:

y=0.2*4^(x)

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)

OrdinaryOrange · Answer 2 · 2023-11-11T14:22:42+0000

Answer:

y=(0.2)4^x

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

$\implies0.2=a * 1$

$\implies a=0.2$

Therefore,
y=(0.2)b^x

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

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

$\implies0.8=(0.2)b$

$\implies b=(0.8)/(0.2)$

$\implies b=4$

So the final exponential equation is:

y=(0.2)4^x

Checking the equation with the remaining two points:

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

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