Question

Select all the correct locations on the table

Answer 1

1. exponential decay because when the different years goes by it drops to low prices.
2. exponential decay again becaise the laptops battery goes form 100% to 60% then to 20%
3. linear because it shows a constant rate of change with the tigers.

Answer 2

(i) Exponential Decay

(ii)linear

(iii)Exponential Growth

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
`C=C_(0) e^(-kt)`

Now substitute the values in the above formula

`17500=25000 e^(-k*2)`

Now on simplification, we get

`k=0.1783`

Now again apply the same formula for the next time interval

`12250=25000 e^(-k*4)`

Now on simplification, we get

`k=0.1783`

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
`P=P_(0) e^(kt)`

Now substitute the values in the above formula

`30=20 e^(-k*5)`

Now on simplification, we get

`k=-0.081`

Now again apply the same formula for the next time interval

`45=20 e^(-k*10)`

Now on simplification, we get

`k=-0.081`

Since the value of k is constant for both the time interval. Hence the decays is exponential.