Question

Recall the hurricane relief fund context from the previous investigation. Bob set up a hurricane relief donation fund and started it off by donating $ 35 . Instead of tripling in value each day, suppose it doubled in value each day

Answer 1

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Complete Question

Recall the hurricane relief fund context from the previous investigation. Bob set up a hurricane relief donation fund and started it off by donating $ 35 . Instead of tripling in value each day, suppose it doubled in value each day

Complete the following table showing the account values at the end of each day.

Number of days since the initial investment, n Amount (in dollars) in the relief account, A

0 1 2 3 4

Answer:

Number of days(n) = Amount (in dollars) in the relief account(A)

0 = $35

1 = $70

2 = $140

3 = $280

4 = $560

Step-by-step explanation:

The formula for doubling time

P(t) = Po(2)^t/k

Where P = Amount after time t

Po = Initial Amount

t = number of days

k = Frequency at which it doubles

For 0 days

t = 0, k = 1, P(o) = $35

P(t) = Po(2)^t/k

P(0) = $35(2)^0/1

= $35(2)⁰

= $35 × 1

= $35

For 1 day

t = 1, k = 1 , P(0) = $35

P(t) = Po(2)^t/k

P(0) = $35(2)^1/1

= $35(2)¹

= $35 × 2

= $70

For 2 days

P(t) = Po(2)^t/k

t = 2, k = 1, P(0) = $35

P(0) = $35(2)^2/1

= $35(2)²

= $35 × 4

= $140

For 3 days

P(t) = Po(2)^t/k

t = 3, k = 1

P(0) = $35(2)^3/1

= $35(2)³

= $35 × 8

= $280

For 4 days

P(t) = Po(2)^t/k

t = 3, k = 1, P(0) = $35

P(0) = $35(2)^5/1

= $35(2)⁴

= $35 × 16

= $560