The population of bacteria is being measured. The equation log10P=0.5t+1.398\log_{10}P = 0.5t + 1.398log10P=0.5t+1.398 is used to model the population of bacteria, PPP, t t\,t hours after it was first recorded.
Show that P=abtP = ab^tP=abt, where a a\,a and b b\,b are constants to be found. Give the value of a a\,a to the nearest whole number and give the value of b b\,b to 3 significant figures.
Interpret the meaning of the constant a a\,a in this model.
Find the population of the bacteria after 10 hours. Give your answer to 2 significant figures.
