Question

I need an equation for this algebra problem

Answer 1

Answer:

2.5 hours

Step-by-step explanation:

Given

The information in the attachment

To solve this question, first we calculate the slope

$(t_1,B_1) = (1,19,5\%)$

$(t_2,B_2) = (2,13\%)$

The slope is:

$m = \frac{B_2 - B_1}{t_2 - t_1}$

$m = \frac{13\% - 19.5\%}{2-1}$

$m = \frac{-0.065}{1}$

$m = -0.065}$

The equation is calculated as:

$B - b_3 = m(t - t_3)$

Where

$m = -0.065}$

$(t_3,B_3) = (3,6.5\%)$

This gives

$B - 6.5\% = -0.065(t - 3)$

$B - 6.5\% = -0.065t +0.195$

$B -0.065 = -0.065t +0.195$

$B = -0.065t +0.195 +0.065$

$B = -0.065t +0.26$

To calculate the time at 9.75%.

We take B = 9.75%

So, we have:

$9.75\% = -0.065t +0.26$

Solve for t

$0.0975= -0.065t +0.26$

Collect Like Terms

$0.065t= -0.0975 +0.26$

$0.065t= 01625$

$t = 0.1625/0.065$

$t = 2.5$

Hence, it will take 2.5 hours.