A car has a purchase price of $24,800. The value declines continuously at an exponential rate of %23 annually. A. Wat is an equation modeling the valu

Ernstfalld 2020-11-02 Answered
A car has a purchase price of $24,800. The value declines continuously at an exponential rate of %23 annually. A. Wat is an equation modeling the value of this car after t years? B. What is its value after 6 years? c. How long will it take for its value to be $2000? 2. A bacteria colony grows continuously at an exponential rate. There are initially 1.1 million sent. After 5 days, there are 6.8 million present . a. What is the an equation modeling the number of bacteria present after d days? b. How many bacteria will be present after 7 days? c. How long will it take the number of bacteria to reach 92 million?
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Malena
Answered 2020-11-03 Author has 83 answers

Step 1: Consider the provided information, A car has purchase on price $24,800 and the value of car declines continuously at an exponential rate of 23% annually.

Step 2: (A) Consider the function for exponential decay is, 
P=P0(1r%)t
=24800(123100)t
=24800(77100)t
=24800(0.77)t Therefore, the exponential funktion is P=24800(0.77)t.

Step 3: (B) Substitute t=6 in above function,
P=24800(0.77)6
$5168.88 Therefore, the prise after 6 years is $5168.88 Step 4: (c) Substitute P=2000 in the above function.
2000=24800(0.77)t
(0.77)t=200024800
(0.77)t=562
tln(0.77)=ln(565)
t=In(562)In(077)
9.6 years Therefore, the time requarite for value of car become $2000 is 9.6 years.

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