In the year 2012, the population of India was about 1.22 billion. The exponential function P(t)=1.22(1.021)^t is used to calculate the India's population t years from the year 2012. Estimate the population t year of India in the 2020. Can someone help me break down this problem thanks
same as the coffee - plug in the value for t
P(2020-2012) = P(8) = 1.22(1.021)^8 = 1.22*1.18 = 1.44 billion
Sure! To estimate the population of India in the year 2020 using the exponential function, we need to substitute the value of t as 8 (since 2020-2012=8) into the function P(t)=1.22(1.021)^t.
Here is how we can break it down:
1. Start with the given exponential function: P(t)=1.22(1.021)^t
2. Substitute t as 8 to find the population in the year 2020: P(8)=1.22(1.021)^8
3. Evaluate the exponential term: (1.021)^8 ≈ 1.0860434
4. Multiply the result from step 3 by the initial population (1.22): 1.0860434 * 1.22 ≈ 1.3267
Therefore, the estimated population of India in the year 2020 is approximately 1.33 billion (rounded to two decimal places).
To solve similar problems with exponential functions, you need to know the initial value (in this case, the starting population of India in 2012) and the rate of growth (in this case, 1.021). You can then substitute the appropriate values into the function to find the population for a given year.