So you are seeing how much time it'll take so you solve for "t", the time.
<span>So you take the formula A=Pe^(rt) </span>
<span>A=2000 because it's the end value </span>
<span>P=20 because it's the starting value </span>
<span>r=.85 since 85%=.85 and .85 is the rate </span>
<span>Plug the values in and you get 2000=20e^(.85t) </span>
<span>What you do is you divide by 20 so you get 100=e^(.85t) </span>
<span>Take the natural logarithm of both sides 'cause of e and a natural log is written as ln so you get </span>
<span>ln 100=.85t ln e and because you can use the power rule you end up with .85t ln e and </span>
<span>ln e=1 so you have ln 100 = .85t so you divide by .85 so (ln 100)/.85=t and t=5.4178472776331 </span>
<span>hours </span>
<span>3. Exponential decay: </span>
<span>A= Pe^(rt) </span>
<span>where </span>
<span>A is the final amount </span>
<span>P is the initial value </span>
<span>r is rate of decay </span>
<span>t is time (years) </span>
<span>Let's say x is the initial amount then (1/2)x=xe^(32r) </span>
<span>I used x because the value isn't given but anyway division by x would give you 1/2=e^(32r) </span>
<span>Take the ln of both sides so ln 1/2=32r ln e and then ln e=1 so ln 1/2=32r. </span>
<span>Divide both sides by 32 and you'd get (ln 1/2)/32=r and r= -0.021660849392498 </span>
<span>4. Another depreciation question. </span>
<span>Each year the item retains 88% of its last-year value. </span>
<span>Solve: 250,000(0.88)^x = 100,000 </span>
<span>0.88^x = 0.4 </span>
<span>x = [log0.4]/[log0.88] </span>
<span>x = 7.168 years </span>
Equation is y= 1.25 x.
Object produced in 1 hour is 75.
<h3>What is equation?</h3>
An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given:
Number y of objects a machine produces is proportional to the time x (in minutes) that the machine runs.
If 5 objects are produced in 4 hours then
equation will be,
y=5/4
or, y= 1.25 x
Now, objects produced in 1 hour is
y= 1.25*60
y= 75 objects
Learn more about equation here:
brainly.com/question/10413253
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You disagree because you cannot write that number as a fraction since there is no number in the ones place when it is solved and turned into a decimal.
To solve this problem we can use proportion, but first its nice to transform our fraction into improper fraction, so
and
Now we can make proportion
--------------------------
of fuel
x-----------------------------
Now we can cross multiply
- its the result
Answer:
1107.
You are rounding up because the number in the tenths slot is over 5.
