Abucket that contains several inches of water is left outside on a rainy day. the height of the water in the bucket that day is given by the function equation h = 4 + 0.5t, where h is the height of the water and t is the time in hours the bucket sits out in the rain.
what is the meaning of the vertical intercept in this equation?
a.
the bucket originally contained 0.5 in. of water.
b.
the bucket originally contained 4 in. of water.
c.
the bucket fills at a rate of 0.5 in./h.
d.
the bucket fills at a rate of 4 in./h.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: