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In 2005, it took 19.65 currency units to equal the value of 1 currency unit in 1915. In 1990, it took only 14.40 currency units to equal the value of 1 currency unit in 1915. The amount it takes to equal the value of 1 currency unit in 1915 can be estimated by the linear function [tex]\( V \)[/tex] given by [tex]\( V(x) = 0.3629x + 14.9866 \)[/tex], where [tex]\( x \)[/tex] is the number of years since 1990. Thus, [tex]\( V(11) \)[/tex] gives the amount it took in 2001 to equal the value of 1 currency unit in 1915. Complete parts (a) and (b) below.

(a) Use this function to predict the amount it will take in 2012 to equal the value of 1 currency unit in 1915.

(b) Use this function to predict the amount it will take in 2019 to equal the value of 1 currency unit in 1915.

Sagot :

GinnyAnsweridn
Certainly! Let's use the given linear function [tex]\( V(x) = 0.3629x + 14.9866 \)[/tex] to predict the amount it will take in 2012 and 2019 to equal the value of 1 currency unit in 1915.

### Step-by-Step Solution:

#### Understanding [tex]\( x \)[/tex]:
In the function [tex]\( V(x) \)[/tex], [tex]\( x \)[/tex] represents the number of years since 1990. Therefore, we need to calculate [tex]\( x \)[/tex] for the years 2012 and 2019.

#### Calculate [tex]\( x \)[/tex] for 2012:
[tex]\[ x_{2012} = 2012 - 1990 = 22 \][/tex]

#### Calculate [tex]\( x \)[/tex] for 2019:
[tex]\[ x_{2019} = 2019 - 1990 = 29 \][/tex]

Now, we will use the function [tex]\( V(x) \)[/tex] to find the amounts for these years.

#### Calculate the value for 2012:
[tex]\[ V(22) = 0.3629 \times 22 + 14.9866 \][/tex]
Using the given function, we find:
[tex]\[ V(22) \approx 22.9704 \][/tex]

Similarly,

#### Calculate the value for 2019:
[tex]\[ V(29) = 0.3629 \times 29 + 14.9866 \][/tex]
Using the given function, we find:
[tex]\[ V(29) \approx 25.5107 \][/tex]

### Summary:
- In 2012: It will take approximately 22.9704 currency units to equal the value of 1 currency unit in 1915.
- In 2019: It will take approximately 25.5107 currency units to equal the value of 1 currency unit in 1915.

Thus, we use the function [tex]\( V(x) \)[/tex] to predict the future values in the years 2012 and 2019.
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