QuestionA city’s population is 820,000 and grows at $0.4\%$ annually. Which model is correct for $t$ years from now? a. $820000(0.04^{t})$ b. $820000(1+0.004)^{t}$ c. $820000(1+0.4^{t})$ d. $820000+1.004^{t}$

Studdy Solution

STEP 1

Assumptions1. The current population of the city is820000. . The population is increasing exponentially at an annual rate of0.4%.
3. We are looking for an expression that models the population of the city t years from now.
4. The exponential growth formula is $(t) =0(1 + r)^t$ , where $(t)$ is the future population, $0$ is the initial population, $r$ is the growth rate, and $t$ is time in years.

STEP 2

We need to find an expression that matches the exponential growth formula. The initial population $0$ is820000, the growth rate $r$ is0.4%, and $t$ is the time in years.

STEP 3

Convert the percentage growth rate to a decimal value.
$0.\% =0.004$

STEP 4

Substitute the values of $0$ and $r$ into the exponential growth formula.
$(t) =820000(1 +0.004)^t$

STEP 5

This expression matches option b. Therefore, the correct answer isb. $820000(1+0,004)^{t}$ .

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