A farming community begins with one resident. Then every year, the number of residents multiplies by 10 Write an expression using an exponent to represent the number of residents in the community after 5 years

After 10 years , the number of residents in the community = 100,007.45

Step-by-step explanation:

Let P be the population of a farming community.

As we know that,

Exponential Growth model is :

P(t) = P₀      ........(1)

where P₀ is the initial state , k is the growth constant.

As given,

A farming community begins with one resident.

⇒At t = 0 , P(t) = 1

∴ Put t = 0 in equation (1), we get

1 = P₀

⇒1 = P₀

∴  equation (1) becomes

P(t) =    ......(2)

As given, every year, the number of residents multiplies by 10

⇒At t = 1 , P(t) = 10

∴ Put t = 1 in equation (2), we get

10 =

Taking ln both side we get

ln(10) = ln( )

⇒2.3026 = k

∴  equation (2) becomes

P(t) =

Now, we have to find the population at t = 5

⇒P(5) =

So, we get

After 10 years , the number of residents in the community = 100,007.45

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9