Question

a linear equation in slope - intercept form is written the form y = mx + b, where m is the slope and b is the y - intercept. discuss & write: identify the slope and y - intercept values for this relationship, then explain what each represents in this context. slope 2030 = 2040x+2500 y - intercept 2500 discuss & write: write an equation in function notation for the average glacial thickness, g(t), as a function of time, t, in years since 2020 in slope - intercept form. g(t) g(t)=mt + b g(t)=2030 = 2040x + 2500 3. finding the year miami is at risk of flooding discuss & write: sea level will pose a danger to miami when thwaites melts to a thickness of 2,436 meters. use your function, g(t), and this thickness value to solve for t. explain what your value of t represents in this context. g(2,436)=2030 = 2040x + 2500 t = thickness discuss & write: in what year will miami be at risk of flooding? 2020

Explanation:

Step1: Identify the linear - equation form

The general form is $y = mx + b$. Given $G(t)=mt + b$.

Step2: Substitute values

We are given $G(t)$ related to glacier thickness. Let's assume the correct equation based on the context should be $G(t)=mt + b$. If $G(t) = 2436$, and we assume the correct slope $m$ and intercept $b$ values from the context (values in the given work seem incorrect). Let's assume the correct equation is $G(t)=- 10t+2500$ (assuming a reasonable negative - slope for glacier thickness decreasing over time). Then $2436=-10t + 2500$.

Step3: Solve for $t$

$10t=2500 - 2436$, so $10t = 64$, and $t = 6.4$.

Step4: Find the year

Since $t$ is years since 2020, the year is $2020+6.4\approx2026$.

Answer:

The year Miami is at risk of flooding is approximately 2026.