The price of products may increase due to inflation and decrease due to depreciation. derek is studying the change in the price of two products, a and b, over time.
the price f(x), in dollars, of product a after x years is represented by the function below:
f(x) = 0.69(1.03)x
part a: is the price of product a increasing or decreasing and by what percentage per year? justify your answer. (5 points)
part b: the table below shows the price f(t), in dollars, of product b after t years:
t (number of years) 1 2 3 4
f(t) (price in dollars) 10,100 10,201 10,303.01 10,406.04
which product recorded a greater percentage change in price over the previous year? justify your answer. (5 points)

part a. the general formula for a value in exponential growth is given as:

a = ao (1 + r)^x

where r is the rate of growth of the function.

looking at the given equation, we can say that the price of product a after x years is increasing by a fraction of 0.03 or 3% per year.

part b. we can see that the increase in price is also exponential since the amount increase is not constant. therefore the equation must also be in the form of:

b = bo (1 + r)^x

we use the data in year 2 and 1 to find for the r:

10,201 = 10,100 (1 + r)^1

1 + r = 1.01

r = 0.01

since the growth rate of product b is only 0.01 or 1% per year, therefore product a has greater percentage change in price over the years which is 3% per year.

throw the computer

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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