[填空题]
Peter wants to reach a rock, looet4l)fg4 zn g4;ncw /cated 55 km awag48y,qukf; ri y from his current position, using the stry4r;8 q gi,ufkategy outlined below.
Every hour Peter approaches the rock by a fixed percent of the remaining distance to the rock.
The distance, D, in kilometres, Peter has travelled from his original position, can be modelled by the exponential function
D(t)=a+b($k^{-t}$),t≥0,where t is the time, in hours, since Peter started moving.
1.Explain why a=5.
2.Find the value of b. b =
After one hour, the distance from Peter to the rock is 3.75 km.
3.Find the value of k. k =
4.Find the distance between Peter and the rock after 4 hours.
Peter can be heard when shouting from 200 metres away. km
5.Calculate the time it takes until someone standing on the rock can hear Peter shouting. Round your answer correct to the nearest hour.
