What does x equal when the population reaches 18,000 and when it reaches 13,000?

Question

The population of a city has risen and fallen over a 20-year interval. Its population may be modeled by the function
y = 19,000 + 7,000 sin(0.658x), where the domain is the years since 1980 and the range is the population of the city.

Answer 1

y = 19,000 + 7,000 sin (0.658x)

18,000 = 19,000 + 7000 sin (0.658x)

-1,000 = 7000 sin (0.658x)

-1/7 = sin (0.658x)

 

Use arcsin to determine x.

Same process for 13,000.