Convert the formula Dt 80075 tor the level of Prozac in hr

Convert the formula D(t) = 80(0.75? tor the level of Proz-ac in (hr bloodstream following un initial dose of 80 mg to equivalent formulas with base 10 und base e. Non purchased a four-year-old car for $16,400. When the car was new, it sold fur 523,000. a. Find the depredation rate to the nearest tenth or a percent. Show all your work, b What is the exponential depreciation formula? What is your dependent variable and independent variable alongside the symbols used? How long will it take to loose half of the value of the car? Solve algebraically. Solve part c graphically aid copy here the graph labeling the answer and the x and y axis.

Solution

1. D(t) = 80(0.75)^t

where 80 mg is an equivalent amount

Take log to base 10 on both sides:

log(D(t) = log80(0.75)^t

= log80 + t*log0.75

Now with natural log to basee

ln(D(t) = ln(80(0.75)^t

ln(D(t)  = ln(80) + t*ln(0.75)

2. New car price = $ 23000

After 4 years car price =$ 16400

a) Depreciation rate = (present price - original price)/no. of years x 100

= ( 16400 -23000)/4 x 100

= -$1650 per year function

b) Exponential:

Let the function be represented by :

y = a(b)^t

16400 = 23000(b)^4

b = 0.918

So, y = 23000(0.918)^t -----(Depreciation formula)

c) independent variablependent is time t and dependent variable is y ( value of car in $)

d) Time to loose half of the original price

I assum half of price when it was new = 23000/2 = $11500

So, 11500 = 23000(0.918)^t

0.5 = 0.918)^t

taking log of both sides:

ln(0.5) = t*ln0.918

t = 8.1 years