Real life applications of chain rule

The Chain Rule can also help us deduce rates of change in the real world. From the Chain Rule, we can see how variables like time, speed, distance, volume, and weight are interrelated. A horse is carrying a carriage on a dirt path.

See below for an example.

Step-by-step explanation:

The distance travelled by a particle at time t is given by the function

f(t) = (2t - 2)^3  

Find it's velocity at time 2.

Finding the derivative using the chain rule:

f'(t) = 3(2t - 2)^2 * 2 = 6(2t - 2)^2

At time 2 seconds velocity = 6(2*2 - 2)^2 = 24.

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.

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step-by-step explanation: