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.)
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.)

A) In 2014, it will be 24.64 currency units while in 2021, it will be 27.56 currency units.

B) 2051.

Step-by-step explanation:

The currency units are determined using the equation below

Currency Unit = 0.4164(x) + 14.6512. (x being the difference between the year you want to determine the currency unit and 1990)

A) For year 2014,

    x= 201 4-1990= 24

   0.4164(24) + 14.6512 = 24.6448

 Rounding to 2 decimals is 24.64 currency units.

  For year 2021,

  x = 2021-1990 = 31

0.4164(31) + 14.6512 = 27.5596

Rounding to 2 decimals is 27.56 decimals

B) Using the function

Currency Unit = 0.4164(x) + 14.6512. to predict the number of years it will take the 40 Currency units to equal 1 currency unit in 1990,

substitute 40 into currency unit:

40 = 0.4164(x) + 14.6512

40-14.6512= 0.4164(x)

25.3488=0.4164(x)

Dividing both sides by the coefficient of x

x = 25.3488/0.4164 = 61

To get the exact year, add the value of x to 1990

1990+61= 2051

By 2051, the Currency unit of 40 will equal 1 currency note of 1919.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places