A bomb falls with velocity v(t)=C(1−e−kt), where C and k are constants. What is the terminal velocity of the bomb? That is, what is the maximum valocity the bomb can reach regardless of the height of the bomber?

The terminal velocity is equal to C.

Explanation:

Making the assumption that k and t are positive, we then have that -kt is negative. The value of e^(-kt) will be equal to 1/(e^(kt))

If t increases, e^(kt) will increase exponentially and its reciprocal 1/(e^(kt)) will approach zero.

So, we have:

v(t) = C*(1-0)

v(t) = C*(1)

v(t) = C

Therefore, C is the terminal velocity.

the skeletons of most mammals reach a certain size and then stop growing. however, many animals, including some mammals, keep growing throughout their lives. kangaroos, for example, just keep growing and growing until they die. also, the longer an animal lives the greater the chance it might catch some deadly disease.

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