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MissTica
3 years ago
10

A​ country's travel exports​ (good and services that international travelers buy while visiting the​ country) are increasing exp

onentially. The value of such​ exports, t years after​ 2011, can be approximated by ​V(t)equals111.83 e Superscript 0.088 t​, where V is in billions of dollars. ​a) Estimate the value of the​ country's travel exports in 2018 and 2020. ​b) Estimate the growth rate of the​ country's travel exports in 2018 and 2020.
Business
1 answer:
nasty-shy [4]3 years ago
5 0

Answer:

(a)In 2018, V(t)=$207.05 billion

In 2020, V(t)=$246.90 billion

(b)The export growth rate in 2018 is $18.22 billion per year

The export growth rate in 2020is $21.73 billion per year

Explanation:

The value of exports, t years after 2011 can be approximated by:

V(t)=111.83 e^{0.088 t}

(a)We want to estimate the value of the country's travel exports in 2018 and 2020.

Now, 2018-2011=7 years

Therefore, in 2018

V(7)=111.83 e^{0.088 *7}\\=\$207.05$ billion

Now, 2020-2011=9 years

Similarly, in 2020

V(9)=111.83 e^{0.088 *9}\\=\$246.90$ billion

(b)Growth rate

If V(t)=111.83 e^{0.088 t}, then:

V'(t)=111.83(0.088) e^{0.088 t}\\V'(t)=9.84104 e^{0.088 t}

Growth rate in 2018 (at t=7)

V'(7)=9.84104 e^{0.088*7}\\=\$18.22$ billion per year

Growth rate in 2020 (at t=9)

V'(9)=9.84104 e^{0.088*9}\\=\$21.73$ billion per year

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1. Debit Pledges Receivable $700,000

  Credit Pledges Revenue $700,000

To record unrestricted pledges received.

1. Debit Uncollectible Expense $56,000

  Credit Allowance for Uncollectibles $56,000

To record 8% of uncollectible pledges.

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5. Debit Building Mortgage $3,000

   Credit Unrestricted net assets $3,000

To record the payment of mortgage on buildings.

6. Debit Unrestricted net assets $27,200

   Debit Temporarily restricted net assets $5,400

   Credit Interest and dividends Revenue $32,600

To record the receipt of interest and dividends.

6. Debit Permanently restricted net assets $1,000

   Debit Unrestricted net assets $5,000

   Credit Sale of Endowment Investment $6,000

To record the sale and gain of endowment investments.

7. Debit Depreciation Expense:

  Community services $ 12,000

  Public health education $7,000

  Research $10,000

  Fundraising $15,000

  General and administrative $9,000

Credit Accumulated Depreciation $53,000

To record depreciation expense for the year.

8. Debit Other expenses:

 Community services $ 250,600

 Public health education $100,000

 Research $81,000

 Fundraising $39,000

 General and administrative $61,000

Credit Unrestricted net assets $531,600

To record other expenses.

Debit Clerical services expense $2,400

Credit Donated clerical services $2,400

To record the receipt of donated clerical services.

b. Statement of Activities for the year ended December 31, 20X2:

Revenue:

Pledges                                  $700,000

Interest and dividends              32,600

Sale of Endowments                   6,000   $738,600

Depreciation expense:

  Community services           $ 12,000

  Public health education        $7,000

  Research                              $10,000

  Fundraising                          $15,000

  General & administrative      $9,000       53,000

Other expenses:

 Community services        $ 250,600

 Public health education     $100,000

 Research                               $81,000

 Fundraising                          $39,000

 General and administrative $61,000      531,600

Clerical services expense                          $2,400

Change in net assets                              $151,600

Explanation:

a) Data and Calculations

1. Unrestricted net assets

Beginning balance           $ 281,000

Pledges receivable            520,000        

Office equipment                (15,000)

Building mortgage               (3,000)

Interest and Dividends       27,200

Sale of Endowment              5,000

Other expenses              (531,600)

Ending balance             $278,600

2. Temporarily restricted net assets

Beginning balance            $ 87,000

Restricted use grants      $150,000

Interest and Dividends          5,400

Ending balance               $242,400

3. Permanently restricted (endowment) net assets

Beginning balance          $ 219,000

Gain from Endowment           1,000

Ending balance               $220,000

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