The population of Red Hook is growing at a rate of 3.5% per year. If it’s current population is 12,500, in how many years will the population exceed 20,000? Round your answer to the nearest year.

14 years approx.

Step-by-step explanation:

Apply a variation of the compound interest formula:

A = P(1 + r)^t

Let A = 20000 = 12500(1 + 0.03)^t

We are to find t.

Dividing both sides of the above equation by 12500 yields:

1.6 = 1.03^t

Taking the logarithm of both sides, we get:

log 7500 = t log 1.035, which works out to:

 log 1.6

= t = 13.66 years or 14 years approximately

 log 1.03

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .