Which choice shows the best estimate of the product 0.51 × 783?

a.1/2 × 800

b.1 × 1,000

c.5 × 700

d.50 × 800

Step-by-step explanation:

We are given to ask a product of 0.51x783

If we want to find out the product without actual multiplication we can round off both factors to nearest and do

0.51 is very near to

783 rounded off would be 800 since

So the product would be approximately

i.e. option A

Option B is incorrect because 1000 is very far from 783

C is wrong because 700 is not correct round off of 783

D is wrong since 50 is not round off value of 0.51

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.