Question

[terassy]

Could someone please help me in part (iii) of this question. Thanks

1. Gina's application to her bank for a personal loan was successful. She borrowed $7000 to be paid back in equal monthly instalments over five years at 9% per annum, compounding monthly.

(i) How much are Gina's instalments [3m]
(ii) What was the total of Gina's repayments? [1m]
(iii) Calculate the simple interest rate for Gina's loan, correct to one decimal place. [1m]

Answer to part (iii) is 4.9%

Also, when rounding off values should I round up or down in this question, specifically part (ii).

2. A health inspector takes a sample at a food processing plant. She is trying to ascertain the presence of a bacteria and its rate of growth. This is calculated by the formula:

N=N₀e^kt

where N₀ is the intial number of bacteria, t represents time, k represents the rate of growth as a decimal and N is the number of bacteria present at time t.

(i) Initially there are 7000 bacteria present.

Calculate the value of k (correct to three decimal places) if the nunber of bacteria grows to 22 000 in two hours.

(ii) How long will it take the number of bacteria to double in size?

The answer to part (ii) is 12617 bacteria/hour, they rounded up.

Thank you!!

[fun_jirachi]

Could someone please help me in part (iii) of this question. Thanks

1. Gina's application to her bank for a personal loan was successful. She borrowed $7000 to be paid back in equal monthly instalments over five years at 9% per annum, compounding monthly.

(i) How much are Gina's instalments [3m]
(ii) What was the total of Gina's repayments? [1m]
(iii) Calculate the simple interest rate for Gina's loan, correct to one decimal place. [1m]

Answer to part (iii) is 4.9%

Also, when rounding off values should I round up or down in this question, specifically part (ii).

2. A health inspector takes a sample at a food processing plant. She is trying to ascertain the presence of a bacteria and its rate of growth. This is calculated by the formula:

N=N₀e^kt

where N₀ is the intial number of bacteria, t represents time, k represents the rate of growth as a decimal and N is the number of bacteria present at time t.

(i) Initially there are 7000 bacteria present.

Calculate the value of k (correct to three decimal places) if the nunber of bacteria grows to 22 000 in two hours.

(ii) How long will it take the number of bacteria to double in size?

The answer to part (ii) is 12617 bacteria/hour, they rounded up.

Thank you!!

Since you need help for (iii), I'm just going to go ahead and assume you got part (i) and (ii) correct with the correct method. FYI the answers are $145.31 and $8718.51 respectively.
So with simple interest, the formula for the interest is I = PRN, where P is principal, R is rate, N is the number of years. Since we know the amount she needs to pay, we know also the interest she pays which is just
Now you substitute it into the formula I = PRN
And you get your 0.049, which is 4.9%.

For the next question, since it doesn't explicitly state anything, I'm just going to assume t is in hours. So first you substitute the values you know into the equation, and you should be left with one pronumeral k.


Just gonna say rn, the answer that you gave for (ii) makes no sense, because t should be a value, not a rate, since it says HOW LONG. Anyway, you substitute your known values into the equation again like so

So about 1.21 hours, or 72 mins 36 seconds (approximately). Hope this helps!!!

[terassy]

Thank you, it makes total sense now. I accidentally did not put up the question. The answer I was looking for was for question 2 part (iii), where it states:

(iii) How many bacteria are growing each hour when t = 2 hours?

I'm confused on whether I should round up or down.

[fun_jirachi]

You're looking at the rate at which the bacteria grows at t=2.
So your equation rn should look like this:

You differentiate that into
And at t=2, the rate is 12616.94292 bacteria/hour, rounded up to 12617 bacteria/hour.
It gets rounded up because it's closer to 12617 than 12616. The only reason something like that would get rounded down is if it asked for the number of complete bacteria produced per hour, which it doesn't. I dunno really any other way to explain it to you, so if someone can supplement the explanation?
hope this helps

[jamonwindeyer]

I'm confused on whether I should round up or down.

Hey! Here's a bit of a breakdown of rounding as I see it:

- Round normally in almost all cases
- Round down if you are looking at a quantity that can't have parts and you have growth. For example, bacteria or population growth! You can't have parts of a whole, so if you have 375.8 monkeys, you haven't waited long enough to have 376 monkeys. So you have 375 monkeys.
- Round up if you have a quantity that can't have parts and it is decreasing. This is almost always loan repayments or similar. If paying off a loan takes 27.2 months, that means there is still some leftover after the 27th month. You need the 28th month to finish!

Remember this isn't a huge deal either and probably(?) wouldn't cost you marks in an exam

(got your back fun_jirachi)