If a function s (t )gives the position of a function at time t, the derivative gives the velocity, that is, v (t )equalss prime (t ). For the given position function, find (a) v (t )and (b) the velocity when tequals0, tequals5, and tequals8.

a)

b)

We just need to replace the different values of t and see what we got:

t=0,

t =5,  

t=8,

Step-by-step explanation:

Assuming this complete question: "If a function s (t )gives the position of a function at time t, the derivative gives the velocity, that is, v (t)=s'(t ). For the given position function, find (a) v(t) and (b) the velocity when t=0, t=5, and t=8.

"

Part a

The velocity is defined as

And if we derivate the position we got:

Part b

Since we have the function for the velocity:

We just need to replace the different values of t and see what we got:

t=0,

t =5,

t=8,

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.