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Math  /  Algebra

Question2 An African country is seeing its number of species decline at a rate of 3.2\% per year. If the current species count is 2,300,000 species, what will the species count be in 5 years?
A about 1,954,810 species (B) about 2,692,3182,692,318 species (C) about 1,932,000 species (D) about 1,951,836 species

Studdy Solution

STEP 1

Assumptions
1. The current species count is 2,300,000.
2. The decline rate is 3.2% per year.
3. We want to find the species count after 5 years.
4. The decline is compounded annually.

STEP 2

To find the species count after 5 years, we need to use the formula for exponential decay:
N(t)=N0×(1−r)t N(t) = N_0 \times (1 - r)^t
where: - N(t) N(t) is the future species count after t t years. - N0 N_0 is the initial species count. - r r is the annual decline rate. - t t is the number of years.

STEP 3

Substitute the given values into the formula:
- N0=2,300,000 N_0 = 2,300,000 - r=3.2%=0.032 r = 3.2\% = 0.032 - t=5 t = 5
N(5)=2,300,000×(1−0.032)5 N(5) = 2,300,000 \times (1 - 0.032)^5

STEP 4

Calculate (1−0.032) (1 - 0.032) :
1−0.032=0.968 1 - 0.032 = 0.968

STEP 5

Raise 0.968 0.968 to the power of 5:
0.9685 0.968^5

STEP 6

Calculate 0.9685 0.968^5 :
0.9685≈0.854992 0.968^5 \approx 0.854992

STEP 7

Multiply the initial species count by the result from STEP_6:
N(5)=2,300,000×0.854992 N(5) = 2,300,000 \times 0.854992

STEP 8

Calculate the future species count:
N(5)≈2,300,000×0.854992≈1,966,482 N(5) \approx 2,300,000 \times 0.854992 \approx 1,966,482

STEP 9

Compare the calculated species count with the given options:
The closest option to our calculated value of approximately 1,966,482 is option (A) about 1,954,810 species.
The species count after 5 years will be approximately 1,954,810 species.

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