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In 2005, it took 20.26 currency units to equal the value of 1 currency unit in 1919. In 1990, it took only 14.10 currency units to equal the value of 1 currency unit in 1919. The amount it takes to equal the value of 1 currency unit in 1919 can be estimated by the linear function V given by Vx) 0.4164x + 14.6512, where x is the number of years since 1990. Thus, V(11) gives the amount it took in 2001 to equal the value of 1 currency unit in 1919. Complete parts (a) and (b) below.
a) Use this function to predict the amount it will take in 2014 and in 2021 to equal the value of 1 currency unit in 1919 n 2014, it will take currency units. (Round to two decimal places as needed.) In 2021, it will takecurrency units. n 2021, it will tke (Round to two decimal places as needed.) units.
b) When will it take approximately 40 currency units to equal the value of 1 currency unit in 1919? It will take approximately 40 currency units in aboutyears after 1990 to equal 1 currency unit in 1919 (Round to the nearest year as needed.)

Respuesta :

Answer:

a) 24.64 currency units, 27.56 currency units

b) 61 years

Step-by-step explanation:

We are given the following in the question:

The amount it takes to equal the value of 1 currency unit in 1919 can be estimated by the linear function V given by

[tex]V(x) = 0.4164x + 14.6512[/tex]

where x is the number of years since 1990.

a) Amount in 2014

We put x = 24

[tex]V(24) = 0.4164(24) + 14.6512\\V(24) = 24.6448[/tex]

In 2014, it will take 24.64 currency units to equal the value of 1 currency unit in 1919.

Amount in 2021

We put x = 31

[tex]V(31) = 0.4164(31) + 14.6512\\V(31) = 27.5596[/tex]

In 2021, it will take 27.56 currency units to equal the value of 1 currency unit in 1919.

b) We put V(x) = 40

[tex]40 = 0.4164x + 14.6512\\\\x = \dfrac{40-14.6512}{0.4164}\\\\x = 60.876 \approx 61[/tex]

Thus, 40 currency units in 2051 about 61 years after 1990 will be equal to equal 1 currency unit in 1919.

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