# 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? You can still ask an expert for help Expert Community at Your Service • Live experts 24/7 • Questions are typically answered in as fast as 30 minutes • Personalized clear answers Solve your problem for the price of one coffee • Available 24/7 • Math expert for every subject • Pay only if we can solve it ## Expert Answer 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, $⇑$
$P={P}_{0}{\left(1-r\mathrm{%}\right)}^{t}$
$=24800{\left(1-\frac{23}{100}\right)}^{t}$
$=24800{\left(\frac{77}{100}\right)}^{t}$
$=24800{\left(0.77\right)}^{t}$ Therefore, the exponential funktion is $P=24800\left(0.77{\right)}^{t}$.

Step 3: (B) Substitute t=6 in above function,
$P=24800{\left(0.77\right)}^{6}$
$\approx \mathrm{}5168.88$ Therefore, the prise after 6 years is $5168.88 Step 4: (c) Substitute P=2000 in the above function. $2000=24800{\left(0.77\right)}^{t}$ ${\left(0.77\right)}^{t}=\frac{2000}{24800}$ ${\left(0.77\right)}^{t}=\frac{5}{62}$ $t\mathrm{ln}\left(0.77\right)=\mathrm{ln}\left(\frac{5}{65}\right)$ $t=\frac{In\left(\frac{5}{62}\right)}{In\left(\frac{0}{77}\right)}$ $\approx 9.6$ years Therefore, the time requarite for value of car become$2000 is 9.6 years.