\( 1 \leftarrow \) A country's population and the growth rate in 2011 are given below. Use this information and an exponential model to estimate the country's population in the specified year. population \( =159 \) million; growth rate \( =1.564 \) percent, year, 2026 The size of the population in the 2026 will be about (Round to the nearest hundredth as needed.)

To estimate the country's population in 2026 using an exponential growth model, we can apply the formula: \[ P(t) = P_0 \times e^{(r \times t)} \] Where: - \(P(t)\) is the future population, - \(P_0\) is the initial population (159 million), - \(r\) is the growth rate (1.564% or 0.01564 as a decimal), - \(t\) is the time in years from the base year (2026 - 2011 = 15 years). Now, plugging in the values: \[ P(15) = 159 \times e^{(0.01564 \times 15)} \] Calculating the exponent: \[ 0.01564 \times 15 = 0.2346 \] Now, calculate \(e^{0.2346} \approx 1.2646\): \[ P(15) = 159 \times 1.2646 \approx 200.488 \] Thus, the estimated population in 2026 is about **200.49 million** (rounded to the nearest hundredth).