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Answer:
Value of the car after x years
Step-by-step explanation:
Exponential functions are generally expressed in the form: and since this function is decreasing, meaning it has an exponential decay, it can be expressed as:
where r=rate of decay.
In this case the a represents the initial value or y-intercept, since when x=0, (1-r)^0 = 1, so we just have y=a(1) or y=a
The r represents the rate of decay
the x usually represents the time in seconds, days, months, or whatever unit is being used
The y value represents the value of whatever your measuring, and in this context it represents the value of the car after x years.
This is because a represents the initial value
After one year it's only 85% worth it's initial value or 15% less which is represented as 0.85(a)
After two years it's only 85% worth the previous year or 15% less the previous year, which is represented as 0.85(0.85(a))
This will continue to decrease the number of years increase
Answer: 7 years
Step-by-step explanation:
= In2 / ∧
since the half life is given , we have :
22 = In 2/ ∧
∧ = In2/22
∧ = 0.032
Recall the formula for half life:
=
Therefore:
0.80 =
Take the In of both sides
In 0.80 = - 0.032t
t = In 0.80 / - 0.032
t = 7 years