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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 9 months ago

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