Nina's car was worth 15,000 at the beginning of 2000 and the...

Nina's car was worth $15,000 at the beginning of 2000 and the value of the car decreased exponentially, decreasing by 16% each year. a. Write a function f that determines the value of Nina's car (in dollars) in terms of the number of years t since the beginning of 2000. f(t) = 15000(1-0.16)^t b. How many years after the beginning of 2000 was Nina's car worth $6,000? c. How many years after the beginning of 2000 was Nina's car worth $2,000?

Transcript

00:01 In this question, we have given that a chandelier is five foot length and it's hanging in the ceiling which is 35 foot above and it is given that let's say a man six feet tall is standing right directly under the chandelier.

00:35 So let's say that the chandelier c and it's of the height five feet.

00:49 So this is five foot and the man exactly stands right here who is six feet tall and the distance here it is going to be 35 foot.

01:06 So for the first subdivision we have to calculate is how long do you have to get out of the way so that the chandelier does not fall on the head of the man.

01:18 So for that let's say that this is going to be the total one that is y subtracted by y naught is going to be the total foot that is 35 subtracted by height of the man plus the chandelier height.

01:39 So it's going to be 35 subtracted by 11 which is y negative of y naught is going to be 24.

01:46 So v of zero that is the initial velocity zero and here the gravity acts so it is going to be 32.

01:56 So after this let's form the equation which states that y is equals to y y of zero that is y naught is equals to sorry plus v of zero multiplied by the time subtracted by one over two gt squared.

02:20 So let's say y subtracted by y naught is equals to v naught is zero.

02:26 So zero multiplied by t is going to be zero negative of one over two 32 multiplied by t squared.

02:34 So v subtracted by v y subtracted by y naught is 24 is equals to negative one over two multiplied by 32 into t squared.

02:44 So simplifying this we'll be having 16 right here.

02:47 So t squared is equals to 24 over 16 that is in the negative one.

02:56 So here the gravity is of in the negative form as it's falling downwards.

03:02 So this becomes plus.

03:04 So this implies t is equals to square root of 24 over 16.

03:10 So upon simplification we get t is equals to one point two two seconds which is the required answer.

03:17 In the next subdivision it is said that we have to find the speed at which the chandler travels if we haven't moved from that given point.

03:31 So for that let's introduce we let's say that speed is equals to v of zero the whole squared plus two times of gravity g multiplied by y subtracted by y naught...

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