Create a program ( in c++) will prompt the user to enter a time in days and calculate the magnitude of the binary star for that time. Your program should use a simple if to ensure that the entered time is valid (greater than or equal to 0) and prompt the user to re-enter if the entered time is invalid. Then use an if-elseif structure to determine the magnitude for the entered time. Your output should be similar to At _____ days the magnitude of the binary star is _______. Output the days to 3 significant figures and the magnitude to 5 significant figures. Hint: The fmod function will calculate the remainder of floating point division

Problem: Astronomers have measured the magnitude (brightness) of a binary star as a function of time and found it to have periodicity (cycle) of 6.4 days. The magnitude varies as given below.

from times t = 0 days until t = 0.9 days the magnitude is 2.5

from times t = 0.9 days until t = 2.3 days the magnitude may be calculated by the formula

3.355 - ln(1.352 + cos(*(t - 0.9)/0.7))

from times t = 2.3 days until t = 4.4 days the magnitude is 2.5

from times = 4.4days until t = 5.2 days the magnitude may be calculated by the formula 3.598 - ln(1.998 + cos( *( t - 4.4)/0.4))

from times = 5.2 days until t = 6.4 days the magnitude is 2.5 At 6.4 days the cycle begins again as if the time was 0 days.

A graph for 2 cycles (12.8) days is given below.

Can somone please help me with this program?

4.4 4.2 3.8 3.6 3.4 3.2 2.8 2.6 2.4 10 12 14