The total municipal debt for the state of Illinois can be represented as the exponential function M(t)=41.24(1.052)t, where M represents the total municipal debt for the state in billions of dollars and t is the number of years since 2000. Determine the statement that interprets the function M(t).(1 point)
The total municipal debt in Illinois was $43.38 billion in 2000 and increases about 5.2% each year.
The total municipal debt in Illinois was $39.20 billion in 2000 and increases about 105.2% each year.
The total municipal debt in Illinois was $41.24 million in 2000 and increases about 1.052% each year.
The total municipal debt in Illinois was $41.24 billion in 2000 and increases about 5.2% each year.
nonsense, that is not exponential
Perhaps you mean:
M(t)=41.24(1.052)^t
which would be increase by 5.2 % per year starting at 41.24 *10^9
However as written it is meaningless.
thx
The total municipal debt in Illinois was $41.24 billion in 2000 and increases about 5.2% each year.
Well, looks like Illinois knows a thing or two about debt. It's been growing at a 5.2% rate each year since 2000. That's some impressive dedication to owing money!
The statement that interprets the function M(t) is:
"The total municipal debt in Illinois was $41.24 billion in 2000 and increases about 5.2% each year."
The correct statement that interprets the function M(t) is: The total municipal debt in Illinois was $41.24 billion in 2000 and increases about 5.2% each year.
To determine this, we look at the given exponential function M(t)=41.24(1.052)^t, where M represents the total municipal debt for the state in billions of dollars and t is the number of years since 2000.
From the function, we can see that the initial debt in 2000 was $41.24 billion, as it is the constant term in the function. Additionally, we see that the exponential term (1.052)^t represents the percentage increase per year. This means that for each year t after 2000, the debt increases by approximately 5.2%.
Hence, the correct interpretation of the function is that the total municipal debt in Illinois was $41.24 billion in 2000 and increases about 5.2% each year.