Question

Please help in urgent need for this answer

Answer 1

Explanation:

i)

Consider the exponential equation

`y = a {e}^(bt)`

Now Substitute these points to get a and b value

(0,37000) , (1,20350)

`37000 = a * {e}^(b * 0)`

`37000 = a * 1`

Hence a=37000

Now Substitute t=1

`20350 = 37000 * {e}^(b * 1)`

`(20350)/(37000) = {e}^(b)`

`0.55 = {e}^(b)`

`b = log_(e)(0.55) = - 0.5978`

b≈(-0.6)

`y = 37000 {e}^( - 0.6t)`

is the required equation

ii)

`y = 37000 {e}^( - 0.6 * 0.4)`

`y = 37000 {e}^( - 0.24)`

iii) it decreases by a factor of

`{e}^(0.6)`

every decade

So the factor by which the price of car decreases every year is

`{e}^{ (0.6)/(10) }`

as 1year =1/10 decade

Hence the required factor

`{e}^(0.06)`

I hope it helped you