A museum has decided to sell one of its paintings and to invest the proceeds. If the picture is sold between the years 2000 and 2020 and the money from the sale is invested in a bank account earning 5% interest per year compounded annually, then B(t), the balance in the year 2020, depends on the year, t, in which the painting is sold and the sale price P(t).
If t is measured from the year 2000 so that 0 < t < 20 then:
B(t) = P(t)(1.05)^(20−t)
(a) Explain why B(t) is given by this formula.
(b) Show that the formula for B(t) is equivalent to B(t) = (1.05)^20 [(P(t)/(1.05)^t)].
(c) Find B'(10), given that P(10) = 150,000 and P'(10) = 5,000.

.5 lb

step-by-step explanation:

12 in / 6 in =2 in

.25 x 2 = .5 lb

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3