Please help in urgent need for this answer

Question

asked Jun 6, 2023 115k views

1 Answer

Salina · Answer 1 · 2023-06-13T03:03:16+0000

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