in the graph, y takes the place of n and x takes the place of t.
to solve using your scientific calculator, replace t with 0 or 1 or 2 or 3 or 4 or 5 or 6 and find 80 * log(7 + 10 * t)
the log function of your calculator assumes a base of 10, so 80 * log(7 + 10 * t) is the same as 80 * log10(7 + 10 * t)
from the graph, it appears that, as the number of months since launch gets larger, the additional number of complaints gets smaller.
this can be seen on the graph between the months 4 and 5 versus months 5 and 6
the increase in the number of months between 4 and 5 is 6.702 while the increase in the number of complaints between 5 and 6 is 5.616.
based on the formula, the number of additional increases per month will get smaller and smaller as time goes on, with the limit approaching 0, but never quite reaching 0.
for example:
when the number of months since launch is equal to 100, the number of complaints will be 80 * log(7 + 10 * 100) = 240.242 and when the number of months since launch is equal o 101, the number of complaints will be 80 * log(7 + 10 * 191) = 240.586.
that's an increase of 240.586 - 240.242 = .344.
that's a lot smaller than 5.616 which is the increase between months 5 and 6.
for your number 2, you didn't finish explaining what the problem is.
however, if the value of the car reduces exponentially, this means it is being reduced by the same factor each year.
the formula to use if f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the rate of change per time period
n is the number of time periods.
assume the car is reducing by a rate of 10% per year.
that would mean that r is equal to -.10
assume the value of the car was 20,000.
the formula would become f = 20,000 * (1 - .10) ^ n
simplify this to get f = 20,000 * .9 ^ n
every year, the car will be 90% of the value that it was the previous year.
you can graph this by replacing f with y and n with x to get:
y = 20000 * .9 ^ x.
the graph would look like this.
first graph is losing 10% of value each year.
second graph is losing 20% of value each year.
third graph is losing 30% of value each year.
exponential means it's losing by the same rate each year as opposed to straight line which means it's losing by the same amount each year.
