sequence word problem 6 A home was purchased for 180000 Assu

sequence word problem

6. A home was purchased for $180,000. Assume that in value this property will increase 4% each year for the next six years. Find the value of the home in each of those six years. Write a formula for a sequence whose first six terms give those values. Suppose a colony of 5000 bacteria is doubling in size everyday. How many bacteria will there be after: (a) 2 days? (b) 6 days? (c) n days?

Solution

6) home was purchased $ 180,000

value increases 4% each year

a1 = 180,000

a2 = a1 + .04 *a1

value of house in 2nd year = 180,000+.04*180,000= 187200

a3 = a2+ .04*a2

value of house in 3rd year = 187200+.04*187200 = $194688

value of house in 4th year = 194688+.04*194688 = $ 202475.52

value of house in 5th year = 202475.52+.04*202475.52 = $ 210574.54

value of house in 6th year = 210574.54+.04*210574.54 = $ 218997.521

formula for sequence = an = an-1 + .04 *(an-1)