QuestionIf $S(t)=250(1.045)^{t}$ , which statement is true about the initial deposit and interest rate?

Studdy Solution

STEP 1

Assumptions1. The savings in the bank account can be modeled by the function $(t)=250(1.045)^t$ . . The function $(t)$ represents the amount of money in the bank account at time $t$ .
3. The number250 in the function $(t)$ represents the initial amount deposited in the bank account.
4. The number1.045 in the function $(t)$ represents the interest rate of the bank account plus1.
5. The interest rate is compounded annually.

STEP 2

First, we need to interpret the function $(t)=250(1.045)^t$ . The initial amount deposited in the bank account is represented by the coefficient of the exponential term, which is250.
So, the initial amount deposited was $250.

STEP 3

Next, we need to interpret the base of the exponential term in the function $(t)=250(1.045)^t$ . The base of the exponential term,1.045, represents1 plus the interest rate (in decimal form).
So, $1.045 =1 + Interest\, rate$

STEP 4

To find the interest rate, we need to subtract1 from1.045.
$Interest\, rate =1.045 -1$

STEP 5

Calculate the interest rate.
$Interest\, rate =1.045 -1 =0.045$

STEP 6

To express the interest rate as a percentage, we multiply by100.
$Interest\, rate =0.045 \\times100\%$

STEP 7

Calculate the interest rate in percentage.
$Interest\, rate =0.045 \\times100\% =4.5\%$
So, the interest rate is4.5%.

STEP 8

Now, we can compare our findings with the given options. The initial amount deposited was $250 and the interest rate is4.5%.
So, the correct option is (3) The initial amount deposited was $\$250$ and the interest rate is $4.5 \%$ .

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