A population of deer increases at a rate of 4% annually. If the starting population is 800 deer, how long will it take for the population to grow to 1,200? Round your answer to the nearest tenth of a year.

10.4 years

Step-by-step explanation:

A deer population grows at a rate of 4% annually. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^ t

Where

y represents the population after t years.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 800

r = 4% = 4/100 = 0.04

y = 1200

Therefore

1200 = 800(1 + 0.04)^t

1200/800 = (1.04)^t

1.5 = (1.04)^t

Taking log of both sides to base 10

Log 1.5 = log1.04^t = tlog1.04

0.1761 = t × 0.017

t = 0.1761/0.017

t = 10.4 years

25.2

step-by-step explanation:

2+4x6-8/10= 25.2

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3