the increasing global temperature can be modeled by I=0.1e^(0.02t) where I is the increase in global temperature in degrees Celsius since 1990 and t is the number of years since 1990.
How much warmer was it in 2000 than in 1950?
iIn what year will the temp be 4 degrees Celsius warmer than in 1990?
To find out how much warmer it was in 2000 compared to 1950, we can use the given model I = 0.1e^(0.02t) and substitute the values of t for 2000 and 1950.
Step 1: Calculate the increase in temperature for the year 2000.
Substitute t = 2000 into the equation:
I = 0.1e^(0.02 * 2000)
I = 0.1e^40
I ≈ 1096.63
Step 2: Calculate the increase in temperature for the year 1950.
Substitute t = 1950 into the equation:
I = 0.1e^(0.02 * 1950)
I = 0.1e^39
I ≈ 1093.63
Step 3: Calculate the difference in temperature between 2000 and 1950.
Difference = I(2000) - I(1950)
Difference ≈ 1096.63 - 1093.63
Difference ≈ 3 degrees Celsius
Therefore, the temperature in 2000 was approximately 3 degrees Celsius warmer than in 1950.
To find out in which year the temperature will be 4 degrees Celsius warmer than in 1990, we need to set up and solve an equation.
Step 1: Set up the equation.
We need to find the value of t when the increase in temperature (I) is 4 degrees Celsius. Substitute I = 4 into the given equation:
4 = 0.1e^(0.02t)
Step 2: Solve the equation for t.
Divide both sides of the equation by 0.1:
0.1e^(0.02t) = 4
Take the natural logarithm (ln) of both sides to remove the exponential term:
ln(0.1e^(0.02t)) = ln(4)
Apply the properties of logarithms to simplify the equation:
ln(0.1) + ln(e^(0.02t)) = ln(4)
Since ln(e^(0.02t)) simplifies to 0.02t, the equation becomes:
ln(0.1) + 0.02t = ln(4)
Subtract ln(0.1) from both sides of the equation:
0.02t = ln(4) - ln(0.1)
Step 3: Calculate the value of t.
Divide both sides by 0.02:
t = (ln(4) - ln(0.1))/0.02
Using a calculator, evaluate the right side of the equation to find the value of t.
Approximately:
t ≈ 78.75
Therefore, the temperature will be approximately 4 degrees Celsius warmer than in 1990 around the year 2068 (t + 1990 = 78.75 + 1990 ≈ 2068).