Question

In 1870 the average ground temperature in Paris was 11.8°C. Since then it has risen at a nearly constant rate, reaching 13.5°C in 1969.
(a) Express the temperature T (in °C) in terms of time t (in years), where t = 0 corresponds to the year 1870 and 0 ≤ t ≤ 99.

Answer 1

T = T0(r^t)
13.5 = 11.8(r)^99
r^99 = 13.5/11.8 = 1.144
log r^99 = log 1.144
99 log r = log 1.144
log r = log 1.144 / 99 = 0.00059
r = 10^0.00059 = 1.00136

T = 11.8(1.00136)^t