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sesenic [268]
4 years ago
15

A baseball card is originally worth 3$. It increases by 7% every year while the player is still active. After the player retires

it increases 10% every year. If a player remains active for 7 years, how much is the baseball card worth after 20 years?
Mathematics
1 answer:
vfiekz [6]4 years ago
8 0

Answer:

\$16.64

Step-by-step explanation:

we know that

The exponential function while the player is still active is equal to

y=3(1.07)^{x}

where

y ----> is the value of the baseball card

x ----> the time in years

Find the value of y for x=7 years (7 years still active)

y=3(1.07)^{7}=\$4.82

After 20 years

x=20-7=13 years (13 years retired player)

The initial value is \$4.82

The new equation is equal to

y=\$4.82(1.1)^{x}

substitute

x=13 years

y=\$4.82(1.1)^{13}=\$16.64

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4 years ago
Suppose you invest $2000 at annual interest rate of 4.5 % How much money do you have in the account after five years?
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Answer:

Please check the explanation.

Step-by-step explanation:

To find the amount we use the formula:

A=P\cdot \left(1+\frac{r}{n}\right)^{nt}

Here:

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

Given

P=$2000

r=4.5%

n=4

t = 5 years

<em />

<u><em>Calculating compounded quarterly </em></u>

After plugging in the values

A=2000\left(1+\frac{4.5\%\:}{4}\right)^{4\cdot \:5}

A=2000\left(1+\frac{0.045}{4}\right)^{4\cdot \:5}

A=2000\cdot \frac{4.045^{20}}{4^{20}}

A=\frac{125\cdot \:4.045^{20}}{2^{36}}

A = 2,501.50

Thus, If you deposit $2000 into an account paying 4.5% annual interest compounded quarterly, you will have $2501.50 after five years.

<u><em>Calculating compounded semi-annually</em></u>

n = 2

A=2000\left(1+\frac{4.5\%\:}{2}\right)^{2\cdot \:5}

A=2000\left(1+\frac{0.045}{2}\right)^{2\cdot \:5}

A=2000\cdot \frac{2.045^{10}}{2^{10}}

A = 2,498.41

Thus, If you deposit $2000 into an account paying 4.5% annual interest compounded semi-annually, you will have $2,498.41  after five years.

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