A small island in the middle of a river is eroding away. Each year, the island has 85% of the area from the previous year. After
one year the island has an area of 10.2 thousand square yards. Graph the sequence and describe the pattern. How much of the island is left after 6 years?
1 answer:
Answer:
see the attachment for a graph
4.53 thousand square yards remain after 6 years
Step-by-step explanation:
The area can be described by an exponential equation that multiplies the area by 0.85 when the time variable increases by 1 year. Such an equation might be ...
a(t) = 10.2·0.85^(t-1)
The graph of this is attached.
After 6 years, the equation predicts
a(6) = 10.2·0.85^(6-1) ≈ 4.53 thousand square yards
of island will remain.
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Answer:
a) For the 90% confidence interval the value of and
, with that value we can find the quantile required for the interval in the t distribution with df =3. And we can use the folloiwng excel code: "=T.INV(0.05,3)" and we got:
b) For the 99% confidence interval the value of and
, with that value we can find the quantile required for the interval in the t distribution with df =106. And we can use the folloiwng excel code: "=T.INV(0.005,106)" and we got:
Step-by-step explanation:
Previous concepts
The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."
Solution to the problem
Part a
For the 90% confidence interval the value of and
, with that value we can find the quantile required for the interval in the t distribution with df =3. And we can use the folloiwng excel code: "=T.INV(0.05,3)" and we got:
Part b
For the 99% confidence interval the value of and
, with that value we can find the quantile required for the interval in the t distribution with df =106. And we can use the folloiwng excel code: "=T.INV(0.005,106)" and we got: