It looks like the differential equation is
Factorize the right side by grouping.
Now we can separate variables as
Integrate both sides.
You could go on to solve for explicitly as a function of
, but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.
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.