The arch support of a bridge can be modeled by y=−0.0012x2, where x and y are measured in feet. Find the height and width of the arch.

The height and width of the arch which support of a bridge and modeled by the provided function is 1000 ft and 300 ft long respectively.

What is an exponential function?

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The exponential function with dependent variable y and independent variable x can be written as,

[tex]y=ba^x+c[/tex]

Here, a,b and c are the real numbers.

The arch support of a bridge can be modeled by the following function,

[tex]y=-0.0012x^2+300[/tex]

Here, x and y are measured in feet.

The height and width of the arch has to be found out. First, find the x intercept of the function. As at the x intercept, the y equal to zero. Therefore,

[tex]0=-0.0012x^2+300\\0.0012x^2=300\\x=\sqrt{25000}\\x=500[/tex]

As, the graph is symmetric around the y-axis. Thus, the -500 can also be a solution. Now, the width of the arch can be given as,

[tex]w=500-(-500)\\w=1000\rm ft[/tex]

Now similarly at x equal to zero, the function will be,

[tex]y=300[/tex]

Hence, the height and width of the arch which support of a bridge and modeled by the provided function is 1000 ft and 300 ft long respectively.

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