QuestionWhat function represents the world's population P (in billions) $t$ years after 1975, given a 1.9% growth rate? A) $P(t)=4(1.019)^{t}$ B) $P(t)=4(1.9)^{t}$ C) $P(t)=1.19 t+4$

Studdy Solution

STEP 1

Assumptions1. The world's population growth rate is1.9% per year since1945. The world's population was approximately4 billion in19753. We are looking for a function that represents the world's population, in billions of people, t years since19754. The growth is exponential, not linear

STEP 2

The general form of an exponential function is $(t) =0 \times (1 + r)^t$ where- $(t)$ is the population at time $t$ , - $0$ is the initial population, - $r$ is the growth rate, and- $t$ is the time since the initial population was measured.

STEP 3

Given that the world's population was approximately billion in1975, we can set $0 =$ .

STEP 4

The growth rate is given as1.9% per year. In the exponential function, this rate needs to be expressed as a decimal. So, we convert1.9% to0.019.

STEP 5

Substituting the values of $0$ and $r$ into the exponential function, we get $(t) =4 \times (1 +0.019)^t$

STEP 6

implify the expression inside the parentheses $(t) =4 \times (1.019)^t$ This function represents the world's population, in billions of people, t years since1975. Therefore, the correct answer is A) $(t)=4(1.019)^{t}$ .

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QuestionWhat function represents the world's population P (in billions) $t$ years after 1975, given a 1.9% growth rate? A) $P(t)=4(1.019)^{t}$ B) $P(t)=4(1.9)^{t}$ C) $P(t)=1.19 t+4$

Studdy Solution

STEP 1

Assumptions1. The world's population growth rate is1.9% per year since1945. The world's population was approximately4 billion in19753. We are looking for a function that represents the world's population, in billions of people, t years since19754. The growth is exponential, not linear

STEP 2

The general form of an exponential function is $(t) =0 \times (1 + r)^t$ where- $(t)$ is the population at time $t$ , - $0$ is the initial population, - $r$ is the growth rate, and- $t$ is the time since the initial population was measured.

STEP 3

Given that the world's population was approximately billion in1975, we can set $0 =$ .

STEP 4

The growth rate is given as1.9% per year. In the exponential function, this rate needs to be expressed as a decimal. So, we convert1.9% to0.019.

STEP 5

Substituting the values of $0$ and $r$ into the exponential function, we get $(t) =4 \times (1 +0.019)^t$

STEP 6

implify the expression inside the parentheses $(t) =4 \times (1.019)^t$ This function represents the world's population, in billions of people, t years since1975. Therefore, the correct answer is A) $(t)=4(1.019)^{t}$ .

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QuestionWhat function represents the world's population P (in billions) ttt years after 1975, given a 1.9% growth rate? A) P(t)=4(1.019)tP(t)=4(1.019)^{t}P(t)=4(1.019)t B) P(t)=4(1.9)tP(t)=4(1.9)^{t}P(t)=4(1.9)t C) P(t)=1.19t+4P(t)=1.19 t+4P(t)=1.19t+4

Studdy Solution

STEP 1

Assumptions1. The world's population growth rate is1.9% per year since1945. The world's population was approximately4 billion in19753. We are looking for a function that represents the world's population, in billions of people, t years since19754. The growth is exponential, not linear

STEP 2

The general form of an exponential function is(t)=0×(1+r)t(t) =0 \times (1 + r)^t(t)=0×(1+r)twhere- (t)(t)(t) is the population at time ttt, - 000 is the initial population, - rrr is the growth rate, and- ttt is the time since the initial population was measured.

STEP 3

Given that the world's population was approximately billion in1975, we can set 0=0 =0=.

STEP 4

The growth rate is given as1.9% per year. In the exponential function, this rate needs to be expressed as a decimal. So, we convert1.9% to0.019.

STEP 5

Substituting the values of 000 and rrr into the exponential function, we get(t)=4×(1+0.019)t(t) =4 \times (1 +0.019)^t(t)=4×(1+0.019)t

STEP 6

implify the expression inside the parentheses(t)=4×(1.019)t(t) =4 \times (1.019)^t(t)=4×(1.019)tThis function represents the world's population, in billions of people, t years since1975. Therefore, the correct answer is A) (t)=4(1.019)t(t)=4(1.019)^{t}(t)=4(1.019)t.

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QuestionWhat function represents the world's population P (in billions) $t$ years after 1975, given a 1.9% growth rate? A) $P(t)=4(1.019)^{t}$ B) $P(t)=4(1.9)^{t}$ C) $P(t)=1.19 t+4$

The general form of an exponential function is $(t) =0 \times (1 + r)^t$ where- $(t)$ is the population at time $t$ , - $0$ is the initial population, - $r$ is the growth rate, and- $t$ is the time since the initial population was measured.

Given that the world's population was approximately billion in1975, we can set $0 =$ .

Substituting the values of $0$ and $r$ into the exponential function, we get $(t) =4 \times (1 +0.019)^t$

implify the expression inside the parentheses $(t) =4 \times (1.019)^t$ This function represents the world's population, in billions of people, t years since1975. Therefore, the correct answer is A) $(t)=4(1.019)^{t}$ .