A square picture with sides of 32 inches is to be mounted on a square mat with sides of 52 inches. Find the area of the mat that will remain uncovered by the picture.

Step-by-step explanation: this problem will result in difference of two squares.

Firstly since they are both areas, it will be area of the bigger square minus area of the smaller squares.

52² - 32²= (52+32)(52-32)

= (84)(20)

=1680inch².

Therefore the area of the material that will remain uncovered will be

1680inches²

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.