In the setting of Exercise 98, calculate the rate of change of T (in K/yr) if T = 283 K and R increases at a rate of 0.5 Js⁻¹m⁻² per yr.

Data From Exercise 98

Climate scientists use the Stefan–Boltzmann Law R = σT⁴ to estimate the change in the earth’s average temperature T (in kelvins) caused by a change in the radiation R (in joules per square meter per second) that the earth receives from the sun. Here, σ = 5.67 × 10⁻⁸ Js⁻¹m−2K⁻⁴. Calculate dR/dt, assuming that T = 283 and dT/dt = 0.05 K/year. What are the units of dR/dt?