Answer:
(i) Exponential Decay
(ii)linear
(iii)Exponential Growth
Step-by-step explanation:
(i)
Cost of the van=$25,000.
After 2 years, value of van=$17,500.
After 4 years, value of van = $12,250.
Its a decay but to be a exponential decay it must have constant rate.
As its known the exponential decay formula is [tex]C=C_{0} e^{-kt}[/tex]
Now substitute the values in the above formula
[tex]17500=25000 e^{-k*2}[/tex]
Now on simplification, we get
[tex]k=0.1783[/tex]
Now again apply the same formula for the next time interval
[tex]12250=25000 e^{-k*4}[/tex]
Now on simplification, we get
[tex]k=0.1783[/tex]
Since the value of k is constant for both the time interval. Hence the decays is exponential.
(ii)
At the beginning, battery life=100%.
After 3 Hours, battery life=60%.
After 6 Hours, battery life = 20%.
Since the value of battery life decreases by 40% in each interval. Hence the decay of battery life is linear.
(iii)
Initial population=20.
After 5 years, population=30.
After 10 years, population = 45.
Its a growth but to be a exponential growth it must have constant rate.
As its known the exponential growth formula is [tex]P=P_{0} e^{kt}[/tex]
Now substitute the values in the above formula
[tex]30=20 e^{-k*5}[/tex]
Now on simplification, we get
[tex]k=-0.081[/tex]
Now again apply the same formula for the next time interval
[tex]45=20 e^{-k*10}[/tex]
Now on simplification, we get
[tex]k=-0.081[/tex]
Since the value of k is constant for both the time interval. Hence the decays is exponential.
