100 points
could you write a formal proof of this?
2. given: 2x -4 = 6x - 8 prove: x = 1

step-by-step explanation:

2x - 4 = 6x - 8

8 - 4 = 6x - 2x

4 = 4x

1 = x

hey casatellicater!

hope you're doing great today : )

they want us to prove that x actually equals 1. so let's prove.

if you've ever had to 'check your work' on a worksheet, this is exactly the same! so all we need to do is plug in x for 1!

our equation should look like: 2(1)-4=6(1)-8

i'm sure you know how to solve from there, can you do it? if you struggle just let me know below! : )

check your work with me when you finished solving.

k = 1

P(t) = (t + 20)²

Step-by-step explanation:

P' = k√P = k P⁰•⁵

To solve for k,

P' = 10 rabbits/month

P = 100 rabbits

10 = k √100

10 = 10k

k = 1

To solve for P(t)

P' = dP/dt

(dP/dt) = kP⁰•⁵

dP/P⁰•⁵ = k dt

P⁻⁰•⁵ dP = k dt

∫ P⁻⁰•⁵ dP = ∫ k dt

2P⁰•⁵ = kt + c

At t = 0, P = 100

2(100)⁰•⁵ = 0 + c

2 × 10 = c

c = 20

2P⁰•⁵ = kt + c

2P⁰•⁵ = kt + 20

Recall, k = 1

2P⁰•⁵ = t + 20

P⁰•⁵ = (t + 20)

P(t) = (t + 20)²