A quantity P obeys the exponential growth law P(t)=e5t (t in years). At what time t0 is P=15? Use yr for years. t0=?
At what time t1 is P=20? Use yr for years. t1= ?
What is the doubling time for P? Use yr for years. The doubling time is ?

the time at which P =15 is

the time at which P =20 is

the doubling time

Step-by-step explanation:

From the information we are being provided with:

The quantity P i.e

In order to determine the time at which P = 15, we have the following:

   when P = 15

∴

Hence, the time at which P =15 is

In order to determine the time at which P = 20, we have the following:

   when P = 20

∴

Hence, the time at which P =20 is

The doubling time at t = 0, mean P = 2

∴

Hence, the doubling time

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet