tim explained a function in words and paul wrote an equation. tim the amount of money in a savings account…

tim explained a function in words and paul wrote an equation. tim the amount of money in a savings account increases at a rate of $225 per month. after eight months, the bank account has $4,580 in it. paul y - 1,400 = 56(x + 26) whose function has the smaller y - intercept? tims with a y - intercept of $2,700 pauls with a y - intercept of $2,856 pauls with a y - intercept of $2,800 tims with a y - intercept of $2,780

tim explained a function in words and paul wrote an equation. tim the amount of money in a savings account increases at a rate of $225 per month. after eight months, the bank account has $4,580 in it. paul y - 1,400 = 56(x + 26) whose function has the smaller y - intercept? tims with a y - intercept of $2,700 pauls with a y - intercept of $2,856 pauls with a y - intercept of $2,800 tims with a y - intercept of $2,780

Answer

Explanation:

Step1: Find Tim's y - intercept

Let the linear - function for Tim's savings be $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. The slope $m = 225$ (the rate of increase per month). We know that when $x = 8$, $y=4580$. Substitute into the equation $y=mx + b$: $4580=225\times8 + b$ $4580 = 1800 + b$ $b=4580 - 1800=2780$

Step2: Find Paul's y - intercept

Given the point - slope form of the equation $y - 1400=56(x + 26)$. Rewrite it in slope - intercept form $y=mx + b$: $y-1400=56x+1456$ $y = 56x+1456 + 1400$ $y=56x + 2856$ The y - intercept of Paul's function is $2856$.

Step3: Compare y - intercepts

Since $2780<2856$, Tim's function has the smaller y - intercept.

Answer:

Tim's with a y - intercept of $2780$