3) A sample of 42 grams of an unknown substance has a half-life of 1,300 years. (a) Write an equation to determine the amount of substance, S, left after t years.

(b) Approximately how long will it take for 0.2 grams of substance to remain (to the nearest year)?

a)

b) It will take 10,692 years.

Step-by-step explanation:

Exponential function to determine the amount of substance:

An exponential function to determine the amout of substance after t years is given by:

In which A(0) is the initial amount and r is the decay rate, as a decimal.

(a) Write an equation to determine the amount of substance, S, left after t years.

Half-life of 1300 years means that .

We use this to find r. So

Sample of 42 grams means that . So

Replacing A by S, just for notation purposes

(b) Approximately how long will it take for 0.2 grams of substance to remain (to the nearest year)?

This is t when . So

It will take 10,692 years.

english, cause i can’t you

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.