The demand for lumber is increasing exponentially. The amount of timber N, in billion cubic feet, consumed t years after 1997
can be approximated by N(t)=66(1.018)t, where t=0 corresponds to 1997.How much lumber was consumed in 1997? ( in billions cubic feet )How much lumber was consumed in 1998? (round to the nearest hundredth) Estimate the amount of lumber which will be consumed in 2000. (round to the nearest hundredth)Estimate the amount of lumber which will be consumed in 2010. (round to the nearest hundredth)What would the graph of this look like? (round to the nearest hundredth)
1 answer:
Answer:
- 1997: 66.00 billion cubic ft
- 1998: 67.19 billion cubic ft
- 2000: 69.63 billion cubic ft
- 2010: 83.23 billion cubic ft
Step-by-step explanation:
For repetitive calculations, it is convenient to let a spreadsheet or calculator do them. See attached for the table of values and the graph. The graph is that of an exponential curve. Its slope increases at an increasing rate.
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Answer:
Probability that a randomly selected can will have less than 15.5 ounces is 0.1587.
Step-by-step explanation:
We are given that the amount of soda in a 16-ounce can is normally distributed with a mean of 16 ounces and a standard deviation of 0.5 ounce.
<em>Let X = amount of soda</em>
So, X ~ N()
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = mean amount = 16 ounces
= standard deviation = 0.5 ounce
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, the probability that a randomly selected can will have less than 15.5 ounces is given by = P(X < 15.5 ounces)
P(X < 15.5 ounces) = P( <
) = P(Z < -1) = 1 - P(Z
1)
= 1 - 0.8413 = 0.1587
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.8413.</em>
Hence, the probability that a randomly selected can will have less than 15.5 ounces is 0.1587.