[填空题]
Peter wants to reach 1i8sb aa01zre-yrak 0 z:d x4itz(bdgby 9k8:a rock, locatedx yh) (k lhoqu.2jv4r3 55 km away from his current position, using the strategy outlinevlo3jk x2y(4 )h.u rqhd 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.
