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

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i