Question

In: Math

Which of the following statements about the general exponential equation y = 600 (1.05)t is true?...

Which of the following statements about the general exponential equation y = 600 (1.05)t is true? (Assume t is time in years, with t = 0 in 1950.) Check all that apply.

A)After 1950, each year the y-value is 1.05 times greater than the previous year.

B)The initial amount of 600 is increasing at a rate of 1.05% each year after 1950.

C)When t = 1, y is 105% of its original value, 600.

D)The initial amount of 600 is increasing at a rate of 5% each year after 1950.

Expert Solution

The General eaponential equation y = 600(1.05)^t.

This is actually the reducing balance method to calculate the final value of an asset, appreciated/depreciated at a certain rate over a period of time. The equation is

A = P(1 (r/100)^t, where we use +r if there is an increase in value, and -r if there is a decrease in value.

P is the principal or Initial value of the asset

A is the final final value of the asset and

t is the time im years.

Therefore y = 600(1.05)^t, can be written as y = 600(1+ 5/100)^t.

So P = 600, the initial amount, the rate is +5%, time is t years, and y is the final value.

A) The Statement says that after 1950 (i.e after each year) the y value is 1.05 times greater than the previous year.

This is correct. When t = 1, we get y = 600 * 1.05 = 630.

Now when we calculate sprcifically for the second year, then again t = 1, but P = 630. Therefore for the 2nd year y = 630 * 1.05 = 661.5

B) This is wrong. The value of 1.05 is because the rate is 5% not 1.05%.

C) This is correct. 105% of original value means 105/100 = 1.05 of its original value, and therefore when t = 1, y = 600 * 1.05 = 630 (there could have been a trick question where the statement is, when t = 1, y is 105% more than its original value of 600. This would then mean 600 * (105 + 100)/100 = 600*205/100 = 1230

D) This is correct. As against the statement of B, the initial amount of 600 is increasing at a rate of 5% every year. This is why our original equation A = P(1 + (r/100)^t for t = 1 and r = 5 becomes and P = 600 becomes 600 (1 + 5/100) = 600 * (105/100) = 600 * 1.05

Therefore A, B and D are true.

milcah answered 8 months ago

1. Which of the following statements about the t-distribution is NOT true? The t-distribution is symmetric...

1. Which of the following statements about the t-distribution is NOT true? The t-distribution is symmetric about 0. The t-distribution has heavier tails than the standard normal distribution. The t-distribution has support on the entire real number line The t-distribution is characterized by two parameters, the mean μ and the variance σ2. 2.Which of the following statements is true? When division by a factor of n-1 is used, the sample variance s2 is an unbiased estimator of the population variance...

Find the general solution of the equation: y^(6)+y''' = t

Find the general solution of this differential equation: y'''+y''+y'+y=4e^(-t)+4sin(t)

Which of the following statements are true and which are false. In general, at a given...

Which of the following statements are true and which are false. In general, at a given temperature, the reaction quotient (Q) is a constant. 1 mol of H2O(g) and 1 mol of CO(g) are placed in a vessel and 1 mol of H2(g) and 1 mol of CO2(g) are placed in another of equal volume. At equilibrium, at 350°C, the amounts of H2O(g) in the two vessels are equivalent. Amounts of all reactants and products corresponding to an exact equilibrium...

Which of the following statements are true about relativistic mass, momentum and energy? T or F?...

Which of the following statements are true about relativistic mass, momentum and energy? T or F? according to Einstein, a particle at rest has no energy at all T or F? if a particle of rest mass m0 were entirely converted into energy, it would yield an energy of (m0)(c^2) T or F? if it were possible to accelerate a particle near the speed of light, its relativistic mass would approach infinity T or F? the relativistic expression for kinetic...

Which of the following statements are true (T) and which are false (F)? a. In the...

Which of the following statements are true (T) and which are false (F)? a. In the Fisher’s exact test we test the following hypotheses: H0: the proportions of type A and type B discordant pairs are the same (pA=pB). H1: the proportions of type A and type B discordant pairs are not the same (pA≠pB). b. Using the McNemar’s test to analyze matched-pair data (paired samples) is a correct decision. c. The Fisher’s exact test is based on a 2x2...

Which one of the following general statements about surplus lines insurance is true? Select one: a....

Which one of the following general statements about surplus lines insurance is true? Select one: a. State guaranty funds do not cover the policyholders of surplus lines insurers b. Surplus lines insurers are subject to state form and rate filing regulations c. All non-admitted insurers are surplus lines insurers d. Admitted insurance companies must write insurance in the surplus lines market

Which of the following statements about correlation are true?

4. Correlation basics Which of the following statements about correlation are true? Check all that apply Correlation is a numerical value between 1.1 and 2. The sign of the correlation indicates the strength or consistency of the linear relationship between two variables. A negative correlation means that two variables tend to change in opposite directions The correlation indicates the strength and the direction of the linear relationship between two variables If the correlation between two variables is 0, there is no clear linear relationship between the...

Which of the following statements about genetics is TRUE?

Which of the following statements about genetics is TRUE? a. A mutation is any change in DNA that is harmful to an organism. b. Genetic disorders are always caused by the inheritance of recessive alleles. c. The red queen hypothesis proposes that asexual reproduction evolved in organisms to increase genetic variation, and therefore, improve resilience in ever-changing environments. d. Natural selection acts directly on the phenotype and indirectly on the genotype.

Find the general solution to the following equation: y''' + 3y''−4y'−6y = cos(t)