A city currently has 153 streetlights. As part of a urban renewal program, the city council has decided to
1 answer:
Answer:
The explicit function is:
And the number of lights after 33 weeks will be 252.
Step-by-step explanation:
Given that:
Total street lights = 153
Let x be the number of weeks
Then the number lights after x weeks will be 3x
This is a linear function where the y-intercept is 153 and slope is 3.
It can be written as: y = mx+b
The function is:
Putting the values for x will give us the number of total lights after that number of weeks.
To find, how many street lights were there at the end of 33rd week,
Putting x = 33
Hence.
The explicit function is:
And the number of lights after 33 weeks will be 252.
You might be interested in
Answer:
The area is growing at a rate of
Step-by-step explanation:
<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>
We identify that the info given on the increasing rate of the circle's radius is 3 and we identify such as the following differential rate:
Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find .
So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):
We now apply the derivative operator with respect to time () to this equation, and use chain rule as we find the quadratic form of the radius:
Now we replace the known values of the rate at which the radius is growing ( ), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :
which we can round to one decimal place as: