Researchers found that the transmission of the COVID-19 virus is affected by the air temperature and relative humidity according to the formula R = 3.968 - 0.0383T - 0.0224H, where R is the reproductive number (a quantity measuring the severity of infectiousness), T is the temperature in degrees Celsius, and H is the relative humidity.

(a) Use this formula to estimate the reproductive number for each of the following combinations of temperature and pressure.

(i) T = 10°, H = 30%
(ii) T = 20°, H = 30%
(iii) T = 10°, H = 55%

(b) What happens to the reproductive number as temperature increases? As relative humidity increases?
(c) An infection will tend to spread when R > 1. Given that H cannot be negative, sketch a region in the plane showing the values of T and H for which the infection will tend to spread.
(d) Sketch a graph of this function in the first octant.