(Solved): 5. The mass, Akg, of algae in a small pond, is modelled by the equation A=pq' where p and q are con ...

5. The mass, Akg, of algae in a small pond, is modelled by the equation A=pq' where p and q are constants and is the number of weeks after the mass of algae was first recorded. k Data recorded indicates that there is a linear relationship between 1 and log, 4 given by the equation log, 4= 0.031+0.5 (a) Use this relationship to find a complete equation for the model in the form A-pq' giving the value of p and the value of q each to 4 significant figures. (b) With reference to the model, interpret (i) the value of the constant p tp. (ii) the value of the constant q. (2) (c) Find, according to the model. (i) the mass of algae in the pond when t=8, giving your answer to the nearest 0.5 kg. (ii) the number of weeks it takes for the mass of algae in the pond to reach 4 kg. "clideo.com (d) State one reason why this may not be a realistic model in the long term. (1) + DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS ARE