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>
Answer:
$0.88
Step-by-step explanation:
cost per 1% = 22 ÷ 100 = 0.22
⇒ cost of 4% = 4 x 0.22 = 0.88
Or
4% = 4/100 = 0.04
⇒ 4% of 22 = 0.04 x 22 = 0.88
Step-by-step explanation:
ANSWER — 350 : 2000 or 7 : 40 (simplified version)
Solving: 100+250=350 (the loan part).
The income is given, it the amount Natalie makes per month (2000).
Simplifying: 350/50=7, 2000/50=40
42÷6=7 42=Perimeter 6=Sides 7=Possible lengths of the hexagon.
Answer:
Step-by-step explanation:
