Question

I need an equation for this algebra problem

Answer 1

2.5 hours

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 = (B_2 - B_1)/(t_2 - t_1)`

`m = (13\% - 19.5\%)/(2-1)`

`m = (-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.