Step-by-step explanation:
i)
Consider the exponential equation
[tex]y = a {e}^{bt} [/tex]
Now Substitute these points to get a and b value
(0,37000) , (1,20350)
[tex]37000 = a \times {e}^{b \times 0} [/tex]
[tex]37000 = a \times 1[/tex]
Hence a=37000
Now Substitute t=1
[tex]20350 = 37000 \times {e}^{b \times 1} [/tex]
[tex] \frac{20350}{37000} = {e}^{b} [/tex]
[tex]0.55 = {e}^{b} [/tex]
[tex]b = log_{e}(0.55) = - 0.5978[/tex]
b≈(-0.6)
[tex]y = 37000 {e}^{ - 0.6t} [/tex]
is the required equation
ii)
[tex]y = 37000 {e}^{ - 0.6 \times 0.4} [/tex]
[tex]y = 37000 {e}^{ - 0.24} [/tex]
iii) it decreases by a factor of
[tex] {e}^{0.6} [/tex]
every decade
So the factor by which the price of car decreases every year is
[tex] {e}^{ \frac{0.6}{10} } [/tex]
as 1year =1/10 decade
Hence the required factor
[tex] {e}^{0.06} [/tex]
I hope it helped you
