Thankyou in advanced, Series help (1 Viewer)

[wandering17]

ANYONE? please

A certain company manufactures three types of shade cloth. The product with code SC50
cuts out 50% of harmful UV rays, SC75 cuts out 75% and SC90 cuts out 90% of UV rays.
In the following questions, you will need to consider the amount of UV light let through.

(a) What percentage of UV light does each cloth let through? = this one i think is just 50%, 25%, 10% yeah

i dont understand how to do the rest?

(b) Show that two layers of SC50 would be equivalent to one layer of SC75 shade cloth.
(c) Use logarithms to find the minimum number of layers of SC50 that would be required
to cut out at least as much UV light as one layer of SC90.
(d) Similarly find how many layers of SC50 would be required to cut out 99% of UV rays.

 

[Ambility]

(b) Show that two layers of SC50 would be equivalent to one layer of SC75 shade cloth.

Just imagine this in your mind: You have 100% of UV rays coming from the sun before they even touch the cloths. Each SC50 cloth just removes half the amount of UV rays directly above it. So the first cloth will remove 50% of the original 100%, allowing 50% to pass through. The second cloth will remove 50% of what's left after the first cloth, which is removing 25% from 50% leaving just 25% of the original UV rays.

(c) Use logarithms to find the minimum number of layers of SC50 that would be required to cut out at least as much UV light as one layer of SC90.

Do you see what I did on that second line of working? I put the number of cloths in the example as an exponent of the percentage it lets through. You can use logarithms to find an unknown in an exponent, and in this situation, we want to find the exponent to show how many cloths we need.



Now we must solve for x, which will tell us the number of layers we need.



And through the change of base formula, you can put this in base 10 or e, and work it out in your calculator, I'll leave this for you to do, but you'll end up with a decimal which doesn't make sense, because we are dealing with whole numbers for the number of cloths we need to use. Just make it the next whole number. 3 cloths won't quite be enough to get you to the same as SC90, but 4 will be your minimum to get past the SC90, if you know what I mean.

(d) Similarly find how many layers of SC50 would be required to cut out 99% of UV rays.

We're just going to do the exact same thing as we did above, except this time we're dealing with a stack of cloth which can cut out at least 99% of rays.



So 6 cloths won't quite be enough, 7 are required.