Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.21 percent a year and that the 1988 population was 6.8 million, write an expression for the population as a function of time in years. (Let t=0t=0 in 1988.)

Question

Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.21 percent a year and that the 1988 population was 6.8 million, write an expression for the population as a function of time in years. (Let t=0t=0 in 1988.)

I got 6.8 e^[0.021(t - 1988)] but it says it's wrong. I don't know what I'm doing wrong.

Answer 1

To find the correct expression for the population as a function of time, we need to use the formula for exponential growth. The general formula for exponential growth is given by:

P(t) = P0 * e^(rt)

Where:
P(t) is the population at time t
P0 is the initial population
r is the growth rate
t is the time in years

In this case, the initial population (P0) in 1988 is 6.8 million, and the growth rate (r) is 0.21 percent, which is equivalent to 0.0021 (expressed as a decimal).

So, the correct expression for the population as a function of time is:

P(t) = 6.8 * e^(0.0021t)

Make sure to use 0.0021 instead of 0.021 in your exponent, as the growth rate should be in decimal form.

Answer 2

To find the expression for the population as a function of time in years, we can use the formula for exponential growth:

P(t) = P0 * e^(rt)

Where:
P(t) is the population at time t
P0 is the initial population
r is the continuous growth rate (in decimal form)
t is the time in years

In this case, the continuous growth rate is given as 0.21 percent, which is equivalent to 0.0021 decimal form. The initial population in 1988 is 6.8 million, so P0 = 6.8.

Substituting these values into the formula, we have:

P(t) = 6.8 * e^(0.0021t)

However, notice that the time variable t is measured from 1988. So, to adjust for this, we need to subtract 1988 from t:

P(t) = 6.8 * e^(0.0021(t - 1988))

So the correct expression for the population of Switzerland as a function of time is:

P(t) = 6.8 * e^(0.0021(t - 1988))

Make sure you check if there are any specific formatting requirements or rounding rules provided in your task, as those might affect the result being marked as correct or incorrect.

Answer 3

That answer is wrong.

Answer 4

It is wrong. Your equation uses a rate of 2.1%. a .21% growth rate means

6.8 * 1.0021^(t-1988)

You can use a base of e, but that would be

ln 1.21 = 0.0021

6.8 e^(0.0021(t-1988))

or, if t is defined as the number of years since 1988,

6.8*1.0021^t
or
6.8 e^(0.0021t)