A school purchases a used van that costs $10,000. The value, V(t), in dollars, of the van t years since its purchase is modeled by the exponential function V(t)=10,000(0.8)^t . Select ALL statements that are true regarding the value of the van. a. The value of the van decreases by 20% each year since its purchase. b. The value of the van decreases by 80% each year since its purchase. c. The value of the van decreases by $2,000 each year since its purchase. d. Each year since its purchase, the value of the van is 80% of the value of the previous year. e. Each year since its purchase, the value of the van is 0.8 times the value of the previous year.

a.The value of the van decreases by 20% each year since its purchase.

b.The value of the van decreases by 80% each year since its purchase.

d.Each year since its purchase, the value of the van is 80% of the value of the previous year.

Step-by-step explanation:

From the above question, we are given the Exponential function

V(t)=10,000(0.8)^t

Verifying the given options:

a.The value of the van decreases by 20% each year since its purchase.

Option a is correct , this is because, the Exponential function above is and Exponential Decrease.

The formula is given as:

V(t) = 10000(1 - r) ^t

Where r = Decreasing rate

Comparing

= 1 - r = 0.8

= 1 - 0.8 = r

r = 0.2

Converting to percentage

= 0.2 × 100 = 20%

Option a is correct

b.The value of the van decreases by 80% each year since its purchase.

Let solve for t = 1 and t = 2

V(t) = 10000(0.8) ^t

When t = 1

= 10000× 0.8¹

= 8000

When t = 2

= 10000× 0.8²

= 6400

Confirming option d

For year 2

= 80% × year 1

Year 1 = 8000

= 80% × 8000 = 6400

Option b is correct

c.The value of the van decreases by $2,000 each year since its purchase.

Option C is incorrect

d.Each year since its purchase, the value of the van is 80% of the value of the previous year.

Option d is correct because

Let solve for t = 1 and t = 2

V(t) = 10000(0.8) ^t

When t = 1

= 10000× 0.8¹

= 8000

When t = 2

= 10000× 0.8²

= 6400

Confirming option d

For year 2

= 80% × year 1

Year 1 = 8000

= 80% × 8000 = 6400

Option d is correct

e.Each year since its purchase, the value of the van is 0.8 times the value of the previous year.

Option e is incorrect

From the options given in the question, the correct statements are,

Options a, b, and d.

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